论文标题
空间形式中完全非线性方程的过度确定问题
Overdetermined problems for fully nonlinear equations in space forms
论文作者
论文摘要
我们研究了子域中完全非线性椭圆方程的过度确定问题$Ø欧几里得球的$ \ $ \ mathbb {s}^{n} $和双曲线空间$ \ mathbb {h} h}^{n} $。我们证明，存在带下划线的方程力$Ø$的经典解决方案是在环境空间中的地理球。我们的结果扩展到完全非线性方程，这是由于Kumaresan和prajapat引起的Laplace操作员的半线性方程式的类似结果。
We study overdetermined problems for fully nonlinear elliptic equations in subdomains $Ø$ of the Euclidean sphere $\mathbb{S}^{N}$ and the hyperbolic space $\mathbb{H}^{N}$. We prove, the existence of a classical solution to the underlined equation forces $Ø$ to be a geodesic ball in the ambient space. Our result extends to fully nonlinear equations, a similar result in the case of semilinear equations with the Laplace operator due to Kumaresan and Prajapat.
