Influence of an L^p-perturbation on Hardy-Sobolev inequality with singularity a curve

2021/02/24 by Thiam, El Hadji Abdoulaye, IJaodoro, Idowu Esther
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.12212

Abstract

We consider a bounded domain Ω of ℝ^N, N≥3, h and b continuous functions on Ω. Let Γ be a closed curve contained in Ω. We study existence of positive solutions u ∈ H¹₀(Ω) to the perturbed Hardy-Sobolev equation: -Δu+h u+bu^1+δ=ρ^-σ_Γu^{2^*_σ-1} \textrm in Ω, where 2^*_σ:=(2(N-σ))/(N-2) is the critical Hardy-Sobolev exponent, σ∈ [0,2), 0< δ

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