Characterization of balls as minimizers of an endpoint Gagliardo seminorm on the boundary

2018/05/09 by Mas, Albert
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.03557

Abstract

Given a bounded C² domain Ω⊂\mathbb R^d with d≥3, we prove a sharp inequality which relates the perimeter of ∂Ω to the endpoint Gagliardo seminorm in W^r,2(∂Ω), corresponding to r=0, of the normal vector field on ∂Ω. The proof of the inequality relies on the use of Bessel potentials and a monotonicity formula; we also show that balls are the unique minimizers. For 1/2

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