Extension method in Dirichlet spaces with sub-Gaussian estimates and applications to regularity of jump processes on fractals
arxiv(2024)
摘要
We investigate regularity properties of some non-local equations defined on
Dirichlet spaces equipped with sub-gaussian estimates for the heat kernel
associated to the generator. We prove that weak solutions for homogeneous
equations involving pure powers of the generator are actually Hölder
continuous and satisfy an Harnack inequality. Our methods are based on a
version of the Caffarelli-Silvestre extension method which is valid in any
Dirichlet space and our results complement the existing literature on solutions
of PDEs on classes of Dirichlet spaces such as fractals.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要