Regularity of solutions to elliptic equations with Grushin's operator
Analysis of PDEs
2019-03-21 v1
Abstract
In this paper, we consider the regularity of solutions to elliptic equation with Grushin's operator. By using the Feynman-Kac formula, we first get the expression of heat kernel, and then by using the properties of heat kernel, the optimal regularity of solutions will be obtained. The novelty of this paper is that the Grushin's operator is a degenerate operator.
Keywords
Cite
@article{arxiv.1903.08371,
title = {Regularity of solutions to elliptic equations with Grushin's operator},
author = {Xiaohuan Wang and Jihui Zhang},
journal= {arXiv preprint arXiv:1903.08371},
year = {2019}
}
Comments
11 pages