Year:

  1.  7
    Existence of Strong Solutions for Quasi-Static Evolution in Brittle Fracture.Jean-François Babadjian & Alessandro Giacomini - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (4):925-974.
    This paper is devoted to prove the existence of strong solutions for a brittle fracture model of quasi-static crack propagation in the two dimensional antiplane setting. As usual, the time continuous evolution is obtained as the limit of a discrete in time evolution by letting the time step tend to zero. The analysis rests on a density lower bound estimate for quasi-minimizers of Mumford-Shah type functionals, under a homogeneous Dirichlet boundary condition on a part of the boundary. In contrast with (...)
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  2.  7
    Quadrature Rules and Distribution of Points on Manifolds.Luca Brandolini, Christine Choirat, Leonardo Colzani, Giacomo Gigante, Raffaello Seri & Giancarlo Travaglini - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (4):889-923.
    We study the error in quadrature rules on a compact manifold. Our estimates are in the same spirit of the Koksma-Hlawka inequality and they depend on a sort of discrepancy of the sampling points and a generalized variation of the function. In particular, we give sharp quantitative estimates for quadrature rules of functions in Sobolev classes.
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  3.  5
    Regularity of Minimizers of Autonomous Convex Variational Integrals.Menita Carozza, Jan Kristensen & Antonia Passarelli di Napoli - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (4):1065-1089.
    We establish local higher integrability and differentiability results for minimizers of variational integrals F = ∫ΩF)dx over W1,p-Sobolev mappings v: Ω ⇢ Rn → RN satisfying a Dirichlet boundary condition. The integrands F are assumed to be autonomous, convex and of growth, but are otherwise not subjected to any further structure conditions, and we consider exponents in the range 1 < p ≤ q < p*, where p* denotes the Sobolev conjugate exponent of p.
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  4.  12
    Some Old and New Results About Rigidity of Critical Metric.Gilles Carron - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (4):1091-1113.
    We present a new proof of a recent ε-regularity of G. Tian and J. Viaclovsky. Our idea also provides a new proof of a classical result of M. Anderson about volume rigidity of Einstein manifolds. Eventually, we also obtain new rigidity results for critical metrics.
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  5.  5
    Isothermalisation for a Non-Local Heat Equation.Emmanuel Chasseigne & Raul Ferreira - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (4):1115-1132.
    In this paper we study the asymptotic behavior for a nonlocal heat equation in an inhomogenous medium: put = J * u - u in RN x, where p is a continuous positive function, u is non-negative and J is a probability measure having finite second-order momentum. Depending on integrability conditions on the initial data u0 and p, we prove various isothermalisation results, i.e. u converges to a constant state in the whole space.
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  6.  2
    The Hopf-Laplace Equation: Harmonicity and Regularity.Jan Cristina, Tadeusz Iwaniec, Leonid V. Kovalev & Jani Onnienen - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (4):1145-1187.
    The central theme in this paper is the Hopf-Laplace equation, which represents stationary solutions with respect to the inner variation of the Dirichlet integral. Among such solutions are harmonic maps. Nevertheless, minimization of the Dirichlet energy among homeomorphisms often leads to mappings which are neither harmonic nor homeomorphism. We prove that such mappings are harmonic outside of a singular set with small image. On the singular set they are locally Lipschitz, but not necessarily differentiable.
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  7.  7
    Uniform Bounds for the Iitaka Fibration.Gabriele Di Cerbo - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (4):1133-1143.
    We give effective bounds for the uniformity of the Iitaka fibration. These bounds follow from an effective theorem on the birationality of some adjoint linear series. In particular we derive an effective version of the main theorem in [19].
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  8.  7
    Dimensionality and the Stability of the Brunn-Minkowski Inequality.Ronen Eldan & Bo'az Klartag - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (4):975-1007.
    We prove stability estimates for teh Brunn-Minkowski inequality for convex sets. As opposed to previous stability results, our estimates improve as the dimension grows. In particular, we obtain a non-trivial conclusion for high dimensions when Voln ≤ 5√Voln Voln. Our results are equivalent to a think shell bound, which is one of the central ingredients in the proof of the central limit theorem for convex sets.
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  9.  4
    Social Choice Among Complex Objects.Luigi Marengo & Simona Settepanella - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (4):1039-1064.
    We present a geometric model of social choice when the latter takes place among bundles of interdependent elements, that we will call objects. We show that the outcome of the social choice process is highly dependent on the way these bundles are formed. By bundling and unbundling the same set of constituent elements an authority enjoys a vast power of determining the social outcome. We provide necessary and sufficient conditions under which a social outcome may be a local or global (...)
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  10.  4
    The Entropy of Nakada's Α-Continued Fractions: Analytical Results.Giulio Tiozzo - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (4):1009-1037.
    We study the ergodic theory of a one-parameter family of interval maps Tα arising from generalized continued fraction algorithms. First of all, we prove the dependence of the metric entropy of Tα to be Hölder-continuous in the parameters α. Moreover, we prove a central limit theorem for possibly unbounded observables whose bounded variation grows moderately. This class of functions is large enough to cover the case of Birkhoff averages converging to the entropy.
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  11.  9
    Bootstrap Regularity for Integro-Differential Operators and its Application to Nonlocal Minimal Surfaces.Begona Barrios Barrera, Alessio Figalli & Enrico Valdinoci - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (3):609-639.
    We prove that C1as-minimal surfaces are of class C∞. For this, we develop a new bootstrap regularity theory for solutions of integro-differential equations of very general type, which we believe is of independent interest.
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  12.  12
    The Corona Theorem for Weighted Hardy and Morrey Spaces.Carme Cascante, Joan Fabrega & Joaquin M. Ortega - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (3):579-607.
    The main goal of this paper is to give a unified proof of the corona theorem for weighted Hardy spaces and for Morrey spaces. We use a technique that reduces the problem to the weighted Hardy spaces H2.
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  13.  5
    Symmetries of F-Manifolds with Eventual Identities and Special Families of Connections.Liana David & Ian A. B. Strachan - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (3):641-674.
    We construct a duality for F-manifolds with eventual identities and certain special families of connections and we study its interactions with several well-known constructions from the theory of Frobenius and F-manifolds.
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  14.  5
    Bubbling Solutions for an Elliptic Equation with Exponential Neumann Data in R^2.Shengbing Deng & Monica Musso - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (3):699-744.
    Let Ω be a bounded domain in R2 with smooth boundary; we study the following Neumann problem where v is the outer normal vector of δΩ, λ > 0 is a small parameter and 0 < p < 2. We construct bubbling solutions to problem by a Lyapunov-Schmidt reduction procedure.
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  15.  5
    Stratified Bundles and Étale Fundamental Group.Hélène Esnault & Xiaotao Sun - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (3):795-812.
    For a smooth projective variety X over an algebraically closed field of characteristic p > 0, we show that all irreducible stratified bundles on X have rank 1 if and only if the commutator [π1, π1] of the étale fundamental group π1 of X is a pro-p-group, and we prove that the category of stratified bundles is semi-simple with irreducible objects of rank 1 if and only if π1 is an Abelian without p-power quotient. This answers positively a conjecture by (...)
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  16.  9
    Normal Forms of Levi-Flat Hypersurfaces with Arnold Type Singularities.Arturo Fernandez-Pérez - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (3):745-774.
    In this paper we study normal forms of Levi-flat hypersurfaces with singularities. We prove a result analogous to the Burns-Georg theorem for the existence of rigid normal forms of Levi-flat hypersurfaces which are defined by the vanishing of the real part of Ak, Dk, Ek singularities.
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  17.  5
    On the Definition and Examples of Finsler Metrics.Miguel Angel Javaloyes & Miguel Sanchez - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (3):813-858.
    For a standard Finsler F on a manifold M, the domain is the whole tangent bundle T M and the fundamental tensor g is positive-definite. However, in many cases, these two conditions hold in a relaxed form only, namely one has either a psuedo-Finsler metric or a conic Finsler metric. Our aim is twofold. First, we want to give an account of quite a few subtleties that appear under such generalizations, say, for conic pseudo-finsler metrics. Second, we aim to provide (...)
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  18.  6
    L^P Estimates for the Wave Equation Associated to the Grushin Operator.Kaur Jotsaroop & Sundaram Thangavelu - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (3):775-794.
    We prove that the solution of the wave equation associated to the Grushin operator G = -Δ - |x|2δt2 is bounded on Lp(Rn+1_, with 1 < p < ∞ when |1/p - 1/2| < 1/n+2.
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  19.  7
    Vanishing of Special Values and Central Derivatives in Hida Families.Matteo Longo & Stefano Vigni - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (3):859-888.
    The theme of this work is the study of the Nekovar-Selmer group H1f attached to a twisted Hida family T† of Galois representations and a quadratic number field K. The results that we obtain have the following shape: if a twisted L-function of a suitable modular form in the Hida family has order of vanishing r ≤ 1 at the central critical point then the rank of H1f as a module over a certain local Hida-Hecke algebra is equal to R. (...)
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  20.  8
    Characterizations of Differentiability for H-Convex Functions in Stratified Groups.Valentino Magnani & Matteo Scienza - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (3):675-697.
    Using the notion of H-subdifferential, we characterize both first and second order differentiability of h-convex functions in stratified groups. Besides some new results involving the h-subdifferential of h-convex functions, we show that all h-differentiability points of an h-convex function, the existence of a second order expansion coincides with a suitable differentiability of its horizontal gradient.
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  21.  5
    On Hilbert's 17th Problem and Pfister's Multiplicative Formulae for the Ring of Real Analytic Functions.Francesca Acquistapace, Fabrizio Broglia & José F. Fernando - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (2):333-369.
    In this work, we present "infinite" multiplicative formulae for countable collections of sums of squares. our formulae generalize the classical Pfisters's ones concerning the representation as a sum of 2r squares of the product of two elements of a field K which are sums of 2r squares. As a main application, we reduce the representation of a positive semidefinite analytic function on Rn as a sum of squares to the representation as sums of squares of its special factors. Recall that (...)
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  22.  4
    On Compactness in the Trüdinger-Moser Inequality. Adimurthi, Tintarev & Cyril - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (2):399-416.
    We show that the Moser functional J = ∫Ω dx on the set B = {u ϵ H10: ||∆u||2 ≤ 1}, where Ω R2 is a bounded domain, fails to be weakly continuous only in the following exceptional case. Define gsw = s-1/2w for s > 0. If uk → u in B while lim inf J > J, then, with some sk → 0, uk = gsk [-1/2 min {1,log 1/|x|}], up to translations and up to a remainder vanishing (...)
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  23.  6
    Semigroups Generated by Elliptic Operators in Non-Divergence Form on C-O.Wolfgang Arendt & Reiner Schätzle - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (2):417-434.
    Let Ω Rn be a bounded open set satisfying the uniform exterior cone condition. Let A be a uniformly elliptic operator given by Au = nΣi,j=1 aij∂iju + nΣj=1 bj∂ju + cu where aji=aij ϵC, and bj, c ϵ L ∞, C ≤ ). We show that the realization A0 of A in C0: = {u ϵ C: u|∂Ω=0} given by D:= {u ϵ C0 ∩ W2,n loc } a0u:= Au generates a bounded holomorphic C0-semigroup on C0. The result is (...)
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  24.  4
    The Integrability of Negative Powers of the Soution to the Saint Venant Problem.Anthony Carbery, Vladimir Maz'ya, Marius Mitrea & David J. Rule - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (2):465-531.
    We initiate the study of the finiteness condition ∫Ωu-Bdx≤C 0 for which the aforementioned condition holds under various hypotheses on the smoothness of Ω and demands on the nature of the constant C. Classes of domains for which our analysis applies include bounded piecewise C1 domains in Rn, n ≥ 2, with conical singularities, polyhedra in R3, and bounded domains which are locally of class C2 and which have outwardly pointing cusps. For example, we show that if uN is the (...)
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  25.  4
    Factoring Threefold Divisorial Contractions to Points.Jungkai Alfred Chen - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (2):435-463.
    We show that any terminal 3-fold divisiorial contraction to a point of index>1 with non-minimal discrepancy may be factored into a sequence of flips, flops and divisorial contractions to points with minimal discrepancies.
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  26.  6
    Monodromy of Lauricella's Hypergeometric $F_A$-System.Keiji Matsumoto & Masaaki Yoshida - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (2):551-577.
    We give a monodromy representation of Lauricella's system of differential equations annihilating the hypergeometric series FA, ; x) of k-variables; its rank is 2k. Under some non-integral conditions for parameters a, =, =, we find circuit matrices with respect to solutions represented by integrals. We make use of the intersection numbers of the domains of the integrals.
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  27.  1
    Monodromy of Lauricella's Hypergeometric FA-System.Keiji Matsumoto & Masaaki Yoshida - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (2):551-577.
    We give a monodromy representation of Lauricella's system of differential equations annihilating the hypergeometric series FA, ; x) of k-variables; its rank is 2k. Under some non-integral conditions for parameters a, =, =, we find circuit matrices with respect to solutions represented by integrals. We make use of the intersection numbers of the domains of the integrals.
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  28.  5
    Formally-Reversible Maps of C^2.Anthony G. O’Farrell & Dmitri Zaitsev - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (2):371-397.
    An element g of a group is called reversible if it is conjugate in the group to its inverse. This paper is about reversibles in the group B = B2 of formally invertible pairs of formal power series in two variables, with complex coefficients. The main result is a description of the generic reversible elements of B2. We list two explicit sequences of reversibles which between them represent all the conjugacy classes of such reversibles. We show that each such element (...)
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  29.  5
    The Eigenvalue Problem for the 1-Biharmonic Operator.Enea Parini, Bernhard Ruf & Cristina Tarsi - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (2):307-332.
    We consider the problem of finding the optimal constant for the embedding of the space W∆2,1:={uϵ W01,1 | ∆u ϵL1} into the space L1, where ΩRN is a bounded convex domain, or a bounded domain with boundary of class C1,a. This is equivalent to finding the first eigenvalue of the 1-biharmonic operator under Navier boundary conditions. In this paper we provide an interpretation for the eigenvalue problem, we show some properties of the first eigenfunction, we prove an inequality of Faber-Krahn (...)
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  30.  9
    Deformation Openness and Closedness of Various Classes of Compact Complex Manifolds; Examples.Dan Popovici - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (2):255-305.
    We review the relations between compact complex manifolds carrying various types of Hermitian metrics and those satisfying topological properties such as the ∂∂-lemma, or the degeneration at E1 of the Frölicher spectral sequence. We also review the behaviour of these properties under holomorphic deformations. The emphasis will be placed on the notion of strongly Gauduchon manifold that we introduced recently in the study of deformation limits of projective and Moishezon manifolds. Besides its expository aspect, the paper presents new results such (...)
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  31.  4
    The Barth Quintic Surface has Picard Number 41.Slawomir Rams & Matthias Schütt - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (2):533-549.
    This paper investigates a specific smooth quintic surface suggested by Barth for it contains the current record of 75 lines over the complex numbers. Our main incentive is to prove that the complex quintic has Picard number 41, and to compute the Néron-Severi group up to a 2-power index. We also compute Picard numbers for reductions to positive characteristic and verify the Tate conjecture.
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  32.  10
    A Priori Estimates and Existence for Elliptic Equations with Gradient Dependent Terms.Nathalie Grenon, François Murat & Alessio Porretta - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (1):137-205.
    We consider, in a bounded domain Ω 1, and the function H grows at most like |Du|q+f, with p-1 (...)
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  33.  4
    A Quantitative Characterisation of Functions with Low Aviles Giga Energy on Convex Domains.Andrew Lorent - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (1):1-66.
    Given a connected Lipschitz domain Ω we let Λ be the set of functions in W2,2 with u=0 on ∂Ω and whose gradient satisfies Vu.nx=1, where nx is the inward pointing unit normal to ∂Ω at x. The functional Iϵ=1/2 ∫Ωϵ-1|1 -|Vu|2|2+ϵV2u|2dz, minimised over Λ, serves as a model in connection with problems in liquid crystals and thin film blisters. It is also the most natural higher order gerealisation of the Modica and Mortola functional. in [16] Jabin, Otto and Perthame (...)
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  34.  5
    On the Vanishing-Viscosity Limit in Parabolic Systems with Rate-Independent Dissipation Terms.Alexander Mielke & Sergey Zelik - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (1):67-135.
    We consider semilinear and quasilinear parabolic systems with a non-smooth rate-independent and a viscous dissipation term in the limit of very slow loading rates, or equivalently with fixed loading and vanishing viscosity ε > 0. Because for nonconvex energies the solutions will develop jumps, we consider the vanishing-viscosity limit for the graphs of the solutions in the extended state space in arclength parameterization. Here the choice of the viscosity norm for parametrization. here the choice of the viscoscity norm for parametrization (...)
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  35.  4
    Unprojection and Deformations of Tertiary Burniat Surfaces.Jorge Neves & Roberto Pignatelli - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (1):225-254.
    We construct a 4-dimensional family of surfaces of general type with pg=0 and K2=3 and fundamental z/2xqg is the quaternion group. The family constructed contains the Burniat surfaces with K2=3. Additionally, we construct the universal coverings of the surfaces in our family as complete intersections on 4 and we also give an action of Z/2xQ8 on 4 lifting the natural action on the surfaces. The strategy is the following. We consider an étale 3-cover T of a surface with pg=0 and (...)
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  36.  14
    A Diameter Bound for Sasaki Manifolds.Yasufumi Nitta - 2014 - Annali della Scuola Normale Superiore di Pisa 13 (1):207-224.
    In this paper we shall show that the diameter of a complete Sasaki manifold whose transverse Ricci curvature is bounded from below by a positive constant has a universal upper bound. This gives another proof of the result of Hasegawa and Seino in [9] which asserts that such manifolds are always compact with finite fundamental group.
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