A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations
A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations
复制标题
DOI：
10.1016/j.anihpc.2005.09.002
复制
发表时间：
2006-09
影响因子：
1.9
通讯作者：
M. Arisawa
中科院分区：
文献类型：
--
作者：
M. Arisawa
给出了有界开域Ω上一类积分微分方程黏度解的一个新定义。我们在边界上考虑狄利克雷边界条件或诺伊曼边界条件。这些方程对应的过程是跳跃和布朗运动的结合。给出了在新框架下粘度解的存在性和比较结果。
We present a new definition of the viscosity solution for a class of integro-differential equations in a bounded open domain Ω in RN. We consider either the Dirichlet boundary condition or the Neumann boundary condition on the boundary. These equations correspond to the process which is a combination of the jumps and the Brownian motion. We give the comparison and the existence results for the viscosity solution in our new framework.