Compact Sobolev embeddings and torsion functions

Lorenzo Brasco (1, 2) , Berardo Ruffini (3)

1 I2M - Institut de Mathématiques de Marseille
2 UniFE - Università degli Studi di Ferrara = University of Ferrara
3 IMAG - Institut Montpelliérain Alexander Grothendieck

For a general open set, we characterize the compactness of the embedding $W^{1,p}_0\hookrightarrow L^q$ in terms of the summability of its torsion function. In particular, for $1\le q

Mots clés: Torsional rigidity; Compact embedding; Hardy inequalities

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Lorenzo Brasco, Berardo Ruffini. Compact Sobolev embeddings and torsion functions. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2017, 34 (4), pp.817 - 843. ⟨10.1016/j.anihpc.2016.05.005⟩. ⟨hal-01620241⟩