Symmetry in Serrin-type overdetermined problems

2025/06/03 by Daomin Cao, Juncheng Wei, Cao, Daomin +3 · 1 citation
Engineering · #Analysis of PDEs (math.AP) #Elasticity and Material Modeling #Elasticity and Wave Propagation #FOS: Mathematics #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.2506.02423

openalex publication_date 2025/06/03 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

This paper investigates the geometric constraints imposed on a domain by overdetermined problems for partial differential equations. Serrin's symmetry results are extended to overdetermined problems with potentially degenerate ellipticity in nonsmooth bounded domains. Furthermore, analogous symmetry results are established for ring-shaped domains. The proof relies on continuous Steiner symmetrization, along with a carefully constructed approximation argument.

Citations

• Rigidity results for the capillary overdetermined problem
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Cited by

• Modica type estimates and curvature results for overdetermined p-Laplace problems

Related

• Counterexamples to Symmetry for Partially Overdetermined Elliptic Problems
• Serrin-type Overdetermined problems in \mathbb Hⁿ
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• A Serrin-type problem with partial knowledge of the domain