Rigidity for the perimeter inequality under Schwarz symmetrisation

2023/06/03 by Domazakis, Georgios
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.02166

Abstract

In this paper, we give necessary and sufficient conditions for the rigidity of perimeter inequality under Schwarz symmetrisation. The term rigidity refers to the situation in which the equality cases are only obtained by translations of the symmetric set. In particular, we prove that the sufficient conditions for rigidity provided in \citefusco2013stability, are also necessary.

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