Serrin-type overdetermined problems for Hessian quotient equations

TL;DR

This paper proves symmetry results for overdetermined boundary value problems involving Hessian quotient equations, extending classical symmetry results to a broader class of fully nonlinear equations.

Contribution

It introduces a new approach using Rellich-Pohozaev identities and P functions to establish symmetry for Hessian quotient equations, generalizing previous results.

Findings

Solutions exhibit symmetry under overdetermined conditions

Established a Rellich-Pohozaev type identity for Hessian quotient equations

Extended symmetry results to Hessian quotient and curvature equations

Abstract

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.