Non-local torsion functions and embeddings

Abstract
Given (Formula presented.), we discuss the embedding of (Formula presented.) in (Formula presented.). In particular, for (Formula presented.) we deduce its compactness on all open sets (Formula presented.) on which it is continuous. We then relate, for all q up the fractional Sobolev conjugate exponent, the continuity of the embedding to the summability of the function solving the fractional torsion problem in (Formula presented.) in a suitable weak sense, for every open set (Formula presented.). The proofs make use of a non-local Hardy-type inequality in (Formula presented.), involving the fractional torsion function as a weight.
Anno
2019
Autori IAC
Tipo pubblicazione
Altri Autori
Franzina G.
Editore
Taylor & Francis
Rivista
Applicable analysis