Wulff shape characterizations in overdetermined anisotropic elliptic\n problems

2017/03/21 by Chiara Bianchini, Giulio Ciraolo, Bianchini, Chiara +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1703.07111

openalex publication_date 2017/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study some overdetermined problems for possibly anisotropic degenerate\nelliptic PDEs, including the well-known Serrin's overdetermined problem, and we\nprove the corresponding Wulff shape characterizations by using some integral\nidentities and just one pointwise inequality. Our techniques provide a somehow\nunified approach to this variety of problems.\n

Citations

• Serrin’s result for hyperbolic space and sphere
• A symmetry problem in potential theory
• Boundary regularity for solutions of degenerate elliptic equations
• Remark on the preceding paper of Serrin
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• Serrin-Type Overdetermined Problems: an Alternative Proof
• A Symmetry Result Related to Some Overdetermined Boundary Value Problems

Cited by

• Optimal Hardy-weights for the Finsler p-Dirichlet integral with a potential

Related

• Some overdetermined problems related to the anisotropic capacity
• Symmetry in Serrin-type overdetermined problems
• Wulff shape symmetry of solutions to overdetermined problems for Finsler Monge-Ampère equations
• An overdetermined problem associated to the Finsler Laplacian
• Serrin's overdetermined theorem within Lipschitz domains