Symmetry results for Serrin-type problems in doubly connected domains

TL;DR

This paper proves rotational symmetry for a class of Serrin-type problems involving the Laplacian in doubly connected domains using a novel technique, offering insights into symmetry results beyond classical methods.

Contribution

It introduces a new approach to establish symmetry in Serrin-type problems, extending the applicability to doubly connected domains and comparing it with classical methods.

Findings

Proves rotational symmetry in doubly connected domains for Serrin-type problems.

Develops a technique based on previous work (arXiv:2109.11255) for symmetry proofs.

Provides a detailed comparison with the classical moving plane method.

Abstract

In this work, we employ the technique developed in arXiv:2109.11255 to prove rotational symmetry for a class of Serrin-type problems for the standard laplacian. We also discuss in some length how our strategy compares with the classical moving plane method.