Wulff shape symmetry of solutions to overdetermined problems for Finsler Monge-Ampère equations

2022/09/07 by Andrea Cianchi, Paolo Salani, Cianchi, Andrea +1
Mathematics · Physics and Astronomy · #35J06 #35J96 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2209.03194

openalex publication_date 2022/09/07 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We deal with Monge-Ampère type equations modeled upon general anisotropic norms H in \mathbb Rⁿ. An overdetermined problem for convex solutions to these equations is analyzed. The relevant solutions are subject to both a homogeneous Dirichlet condition and a second boundary condition, designed on H, on the gradient image of the domain. The Wulff shape symmetry associated with H of the solutions is established.

Related

• An overdetermined problem for the anisotropic capacity
• Some overdetermined problems related to the anisotropic capacity
• Wulff shape characterizations in overdetermined anisotropic elliptic\n problems
• An overdetermined problem associated to the Finsler Laplacian
• An exterior overdetermined problem for Finsler N-laplacian in convex cones