Published Paper
Inserted: 18 may 2015
Last Updated: 24 mar 2021
Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Pages: 29
Year: 2015
Abstract:
For a general open set, we characterize the compactness of the embedding for the homogeneous Sobolev space $\mathcal{D}^{1,p}_0\hookrightarrow L^q$ in terms of the summability of its torsion function. In particular, for $1\le q<p$ we obtain that the embedding is continuous if and only if it is compact. The proofs crucially exploit a torsional Hardy inequality that we investigate in details.
Keywords: compact embedding, Torsional rigidity, Hardy inequalities
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