Serrin-type overdetermined problems for Hessian quotient equations

Serrin-type overdetermined problems for Hessian quotient equations

We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely Hessian quotient equations and Hessian quotient curvature equations. Our approach is based on establishing a Rellich-Pohozaev type identity for Hessian quotient equations and using a P func...

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Veröffentlicht in:arXiv.org 2022-09
Hauptverfasser: Gao, Zhenghuan, Jia, Xiaohan, Zhang, Dekai
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Curvature
Mathematical analysis
Nonlinear equations
Quotients
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description We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely Hessian quotient equations and Hessian quotient curvature equations. Our approach is based on establishing a Rellich-Pohozaev type identity for Hessian quotient equations and using a P function. Our result generalizes the overdetermined problems for k-Hessian equations and k-curvature equations.
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Nonlinear equations
Quotients
title Serrin-type overdetermined problems for Hessian quotient equations
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