In this paper,we prove the symmetry of the solution to overdetermined problem for the equationσ_(k)(D^(2)u-ul)=C^(k)_(n)in hyperbolic space.Our approach is based on establishing a Rellich-Pohozaev type identity and u...In this paper,we prove the symmetry of the solution to overdetermined problem for the equationσ_(k)(D^(2)u-ul)=C^(k)_(n)in hyperbolic space.Our approach is based on establishing a Rellich-Pohozaev type identity and using a P function.Our result generalizes the overdetermined problem for Hessian equation in Euclidean space.展开更多
基金The research is supported by the National Science Foundation of China(No.11721101)the National Key R and D Program of China 2020YFA0713100.
文摘In this paper,we prove the symmetry of the solution to overdetermined problem for the equationσ_(k)(D^(2)u-ul)=C^(k)_(n)in hyperbolic space.Our approach is based on establishing a Rellich-Pohozaev type identity and using a P function.Our result generalizes the overdetermined problem for Hessian equation in Euclidean space.
