Fractional Hardy inequality with singularity on submanifold

2024/07/15 by Adimurthi, Roy, Prosenjit, Sahu, Vivek
#26D15 (Secondary) #46E35 (Primary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.10863

Abstract

We establish fractional Hardy inequality on bounded domains in ℝ^d with inverse of distance function from smooth boundary of codimension k, where k=2, …,d, as weight function. The case sp=k is the critical case, where optimal logarithmic corrections are required. All the other cases of spk are also addressed.

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• Boundary fractional Hardy's inequality in dimension one: The critical case
• Fractional boundary Hardy inequality for the critical cases
• Fractional Hardy-type inequalities in domains with plump complement
• Weighted fractional Hardy inequalities with singularity on any flat submanifold
• The Trudinger type inequality in fractional boundary Hardy inequality