Rigidity for the perimeter inequality under Schwarz symmetrization

IF 1.3 3区数学 Q1 MATHEMATICS

Proceedings of the Royal Society of Edinburgh Section A-Mathematics Pub Date : 2024-06-03 DOI:10.1017/prm.2024.59

Georgios Domazakis

引用次数: 0

Abstract

In this paper, we give necessary and sufficient conditions for the rigidity of the perimeter inequality under Schwarz symmetrization. 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 M. Barchiesi, F. Cagnetti and N. Fusco [Stability of the Steiner symmetrization of convex sets. J. Eur. Math. Soc. 15 (2013), 1245-1278.] are also necessary.

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施瓦兹对称下周长不等式的刚性

本文给出了施瓦茨对称下周长不等式刚性的必要条件和充分条件。所谓刚性是指只有通过对称集的平移才能得到相等情况。我们特别证明了 M. Barchiesi、F. Cagnetti 和 N. Fusco [Stability of the Steiner symmetrization of convex sets.J. Eur.Jur. Math.15 (2013), 1245-1278.] 也是必要条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the Royal Society of Edinburgh Section A-Mathematics 数学-数学

CiteScore

3.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： A flagship publication of The Royal Society of Edinburgh, Proceedings A is a prestigious, general mathematics journal publishing peer-reviewed papers of international standard across the whole spectrum of mathematics, but with the emphasis on applied analysis and differential equations. An international journal, publishing six issues per year, Proceedings A has been publishing the highest-quality mathematical research since 1884. Recent issues have included a wealth of key contributors and considered research papers.