Serrin-type overdetermined problems for Hessian quotient equations
Analysis of PDEs
2022-09-15 v1
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.
Cite
@article{arxiv.2209.06268,
title = {Serrin-type overdetermined problems for Hessian quotient equations},
author = {Zhenghuan Gao and Xiaohan Jia and Dekai Zhang},
journal= {arXiv preprint arXiv:2209.06268},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:2201.04323