TY - JOUR
T1 - Serrin-Type Overdetermined Problems for Hessian Quotient Equations and Hessian Quotient Curvature Equations
AU - Gao, Zhenghuan
AU - Jia, Xiaohan
AU - Zhang, Dekai
N1 - Publisher Copyright:
© 2023, Mathematica Josephina, Inc.
PY - 2023/5
Y1 - 2023/5
N2 - We consider overdetermined problems for Hessian quotient equations and Hessian quotient curvature equations, which are fully nonlinear elliptic equations. We establish Rellich–Pohozaev-type identities for Hessian quotient equations and Hessian quotient curvature equations. Based on these identities and the maximum principle for P functions, the symmetry of solutions can be proved in the Euclidean space. We also prove the related result for Hessian quotient equations in the hyperbolic space. Our results generalize the overdetermined problems for k-Hessian equations and k-curvature equations.
AB - We consider overdetermined problems for Hessian quotient equations and Hessian quotient curvature equations, which are fully nonlinear elliptic equations. We establish Rellich–Pohozaev-type identities for Hessian quotient equations and Hessian quotient curvature equations. Based on these identities and the maximum principle for P functions, the symmetry of solutions can be proved in the Euclidean space. We also prove the related result for Hessian quotient equations in the hyperbolic space. Our results generalize the overdetermined problems for k-Hessian equations and k-curvature equations.
KW - Hessian quotient curvature equation
KW - Hessian quotient equation
KW - Overdetermined problem
KW - P functions
KW - Rellich–Pohozaev identity
UR - https://www.scopus.com/pages/publications/85149200225
U2 - 10.1007/s12220-023-01198-w
DO - 10.1007/s12220-023-01198-w
M3 - 文章
AN - SCOPUS:85149200225
SN - 1050-6926
VL - 33
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 5
M1 - 150
ER -