Fractional boundary Hardy inequality for the critical cases

2023/08/23 by Adimurthi, Roy, Prosenjit, Sahu, Vivek · 2 citations
#26D15 (Secondary) #46E35 (Primary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.11956

Abstract

We establish generalised fractional boundary Hardy-type inequality, in the spirit of Caffarelli-Kohn-Nirenberg inequality for different values of s and p on various domains in ℝ^d, d ≥ 1. In particular, for Lipschitz bounded domains any values of s and p are admissible, settling all the cases in sub critical, super critical and critical regime. In this paper we have solved the open problems posed by Dyda for the critical case sp =1. Moreover we have proved the embeddings of W^s,p₀(Ω) in subcritical, critical and supercritical uniformly without using Dyda's decomposition. Additionally, we extend our results to include a weighted fractional boundary Hardy-type inequality for the critical case.

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• An optimal fractional Hardy inequality on the discrete half-line
• Finsler p-Laplacian in domains becoming unbounded

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