Cari tutti,

questa settimana ci sarà un seminario di analisi di Francesca Prinari (UNIPI):

Giovedì 30 Marzo

Aula Riunioni, ore 17:00

Seguono titolo e abstract.

Un caro saluto,

Alessandra, Jacopo e Maria Stella.

Titolo: Sobolev embedding and distance functions

Abstract:

On a general open set of the euclidean space, we study the relation between the embedding of the homogeneous Sobolev space $D^{1,p}_0$ into $L^q$ and the summability properties of the distance function. We prove that in the superconformal case (i.e. when $p$ is larger than the dimension) these two facts are equivalent, while in the subconformal and conformal cases (i.e. when p is less than or equal to the dimension) we construct counterexamples to this equivalence. In turn, our analysis permits to study the asymptotic behaviour of the positive solution of the Lane-Emden equation for the p-Laplacian with sub-homogeneous right-hand side, as the exponent p diverges to $+\infty$.

(a joint work with L. Brasco and A.C. Zagati).