Mirror symmetry for a Hessian over-determined problem and its generalization

DOI10.3934/CPAA.2014.13.2305zbMath1304.35448OpenAlexW2330547083MaRDI QIDQ479536

Bo Wang, Ji Guang Bao

Publication date: 5 December 2014

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2014.13.2305

zbMATH Keywords

Neumann boundary conditionmoving plane method\(k\)-Hessian equationcorner lemmaWeingarten curvature equation

Mathematics Subject Classification ID

Symmetries, invariants, etc. in context of PDEs (35B06) Overdetermined boundary value problems for PDEs and systems of PDEs (35N25)

Related Items (8)

Serrin-Type Overdetermined Problem in $\mathbb H^n$ ⋮ Radial solutions for fully nonlinear elliptic equations of Monge-Ampère type ⋮ The existence and blow-up of the radial solutions of a \((k_1, k_2)\)-Hessian system involving a nonlinear operator and gradient ⋮ Overdetermined problems for Weingarten hypersurfaces ⋮ The Keller-Osserman problem for the k-Hessian operator ⋮ Serrin-type overdetermined problems for Hessian quotient equations and Hessian quotient curvature equations ⋮ Over-determined problems for \(k\)-Hessian equations in ring-shaped domains ⋮ Symmetry results for viscosity solutions of fully nonlinear equations in annular and exterior domains

Cites Work

• Stability of radial symmetry for a Monge-Ampère overdetermined problem
• On the stability of the Serrin problem
• Serrin-type overdetermined problems: An alternative proof
• Symmetry and related properties via the maximum principle
• Radial symmetry for elliptic boundary-value problems on exterior domains
• Radial symmetry for an electrostatic, a capillarity and some fully nonlinear overdetermined problems on exterior domains
• A symmetry problem in potential theory
• Remark on the preceding paper of Serrin
• Diversifications of Serrin's and related symmetry problems
• Nonlinear second-order elliptic equations V. The dirichlet problem for weingarten hypersurfaces
• Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains
• Elliptic Partial Differential Equations of Second Order
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