论文标题
完全非线性方程的过度确定问题，具有恒定的dirichlet边界条件的空间形式条件
Overdetermined problems for fully nonlinear equations with constant Dirichlet boundary conditions in space forms
论文作者
论文摘要
我们考虑在空间形式的有界域中具有恒定的dirichlet边界条件的两类完全非线性方程的过度确定问题。我们证明，如果域是星形的，那么Hessian商过度确定问题的解决方案是径向对称的。通过为具有恒定的Dirichlet边界条件的$ K $ -Hessian方程建立Rellich-Pohožaev类型的身份，我们还显示了解决方案对$ K $ -Hessian的径向对称性，对于某些边界值而没有星形假设的域名。
We consider overdetermined problems for two classes of fully nonlinear equations with constant Dirichlet boundary conditions in a bounded domain in space forms. We prove that if the domain is star-shaped, then the solution to the Hessian quotient overdetermined problem is radially symmetric. By establishing a Rellich-Pohožaev type identity for the $k$-Hessian equation with constant Dirichlet boundary condition, we also show the radial symmetry of the solution to the $k$-Hessian overdetermined problem for some boundary value without star-shapedness assumption of the domain.
