Compact Sobolev embeddings and torsion functions

2015/06/14 by Brasco, Lorenzo, Ruffini, Berardo · 2 citations
#35P30 #39B72 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1506.04371

Abstract

For a general open set, we characterize the compactness of the embedding W^1,p₀\hookrightarrow L^q in terms of the summability of its torsion function. In particular, for 1≤ q

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• Maz'ya-type bounds for sharp constants in fractional Poincaré-Sobolev inequalities
• Potential Theory and the Boundary of Combinatorial Graphs

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