JS: "There is a robust interest in the history of philosophy and an application of the work of historical philosophers to contemporary issues."

Of a very selective kind, I think. Take my own field - philosophy of art (aka aesthetics). Most analytic philosophers of art leap right over Hegel and go straight to Kant.  Token gestures are sometimes made in the direction of Nietzsche and Schopenhauer but the major emphasis by far is on a small group of eighteenth century philosophers (Kant, Hume etc) and a select group of twentieth century names who are seen as sympathetic to the analytic outlook. (Plato and Aristotle get occasional honorable mention but that goes without saying for all philosophy.)  Key contemporary figures in continental philosophy - Derrida, Levinas, Agamben, Foucault etc - are ignored, along with with earlier names such as Heidegger, Kierkegaard, Sartre, and not surprisingly Marx.

My impression is that something similar is the case for analytic philosophy more generally.

I am not all persuaded by arguments - such as some I've seen on this thread - that claim that the divide is really exaggerated and that, after all, some analytics have an interest in Husserl etc.  One can argue that the number 1 is really not far removed from the number 10 if one starts by saying, well, after all, 4 is not very different from 5, and 4 is close to 3 and therefore not far from 5 either, and 5 is close to 6 .. and so on.  The simple fact remains that there is a huge gulf separating contemporary mainstream analytic philosophy from its contemporary continental counterpart - a gulf reflected in, and perpetuated by, separate journals, conferences etc etc. They are two different countries. There is a DMZ between them where they meet for occasional talks but there is not the slightest sign of reunification...

DA