A fractional Hadamard formula and applications

2020/02/18 by Djitte, Sidy Moctar, Fall, Mouhamed Moustapha, Weth, Tobias · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.07719

Abstract

We consider the domain dependence of the best constant in the subcritical fractional Sobolev constant, λ_s,p(Ω):=inf \ [u]_H^s(ℝ^N)², u∈ C^∞_c(Ω), ‖u‖_L^p(Ω)=1 \, where s∈ (0,1), Ω is bounded of class C^1,1 and p∈ [1, (2N)/(N-2s)) if 2s

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