论文标题
具有空间依赖运算符的非局部方程的粘度解决方案
Viscosity solutions for nonlocal equations with space-dependent operators
论文作者
论文摘要
我们考虑了一类椭圆形和抛物线问题，该问题具有特定的非本地运算符，分数拉普拉斯类型，其中集成在可变域上进行。在粘度意义上，椭圆形和抛物线问题都可以独特地解决。此外，研究了椭圆运算符的某些光谱特性，证明了第一个特征值的存在和简单性。最终，抛物线溶液被证明可以在长期限制下收敛到相应的椭圆溶液。
We consider a class of elliptic and parabolic problems, featuring a specific nonlocal operator of fractional-laplacian type, where integration is taken on variable domains. Both elliptic and parabolic problems are proved to be uniquely solvable in the viscosity sense. Moreover, some spectral properties of the elliptic operator are investigated, proving existence and simplicity of the first eigenvalue. Eventually, parabolic solutions are proven to converge to the corresponding limiting elliptic solution in the long-time limit.
