PDEA Seminar: Compact Sobolev embeddings and asymptotics for the sharp constant

Participate on site or via Zoom link, meeting ID 67226102216.

Abstract: We discuss the relation between the embedding of the homogeneous Sobolev space $D^{1,p}_0$ into $L^q$ (when q \le p) and the summability properties of the distance function of a general open set. Moreover, this analysis permits to study the asymptotic behaviour for the sharp Sobolev-Poincaré constant and for the positive solution of the Lane-Emden equation with the p-Laplacian in the sub-homogeneous case, as p goes to $\infty$.

This is a seminar in the PDEs and Applications seminar series