论文标题
完全非线性椭圆传输问题的粘度解决方案的规律性
Regularity of viscosity solutions to fully nonlinear elliptic transmission problems
论文作者
论文摘要
我们将粘度解决方案的规律性理论用于全线二阶均匀椭圆方程的传输问题。我们的结果提供了完整的存在理论，独特性，比较原则和解决方案界面传输问题的规律性；和$ c^{0，α} $，$ c^{1，α} $和$ c^{2，α} $粘度解决方案的规律性，直至传输表面，对于弯曲接口的情况。
We develop the regularity theory of viscosity solutions to transmission problems for fully nonlinear second order uniformly elliptic equations. Our results give a complete theory of existence, uniqueness, comparison principle, and regularity of solutions to flat interface transmission problems; and the $C^{0,α}$, $C^{1,α}$ and $C^{2,α}$ regularity of viscosity solutions up to the transmission surface for the case of curved interfaces.
