L^p Hardy inequality on C^1,γ domains

2016/11/02 by Lamberti, Pier Domenico, Pinchover, Yehuda
#35B09 #35J92 #49R05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.00563

Abstract

We consider the L^p Hardy inequality involving the distance to the boundary of a domain in the n-dimensional Euclidean space with nonempty compact boundary. We extend the validity of known existence and non-existence results, as well as the appropriate tight decay estimates for the corresponding minimizers, from the case of domains of class C² to the case of domains of class C^1,γ with γ∈ (0,1]. We consider both bounded and exterior domains. The upper and lower estimates for the minimizers in the case of exterior domains and the corresponding related non-existence result seem to be new even for C²-domains.

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