论文标题
分析性差异差异运算符的分析性
Analyticity for Solution of Integro-Differential Operators
论文作者
论文摘要
我们证明，对于某些类别的内核$ k（y）$，integro-differention方程的粘度解决方案$$ \ int _ {\ mathbb r^n}（u（x + y）-2 u（x） + u（x -y））k（y）dy = f（x，u（x））$$如果$ f $是一个分析函数，则是本地分析。这扩展了此类解决方案属于某些Gevrey类的Albanese，Fiscella，valdinoci的结果。
We prove that for a certain class of kernels $K(y)$ that viscosity solutions of the integro-differential equation $$ \int_{\mathbb R^n} (u(x+y) - 2 u(x) + u(x-y)) K(y) dy = f(x,u(x)) $$ are locally analytic if $f$ is an analytic function. This extends the result of Albanese, Fiscella, Valdinoci that such solutions belong to certain Gevrey classes.
