Regularity of solutions to elliptic equations with Grushin's operator

Xiaohuan Wang; Jihui Zhang

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arXiv · 1903.08371

Regularity of solutions to elliptic equations with Grushin's operator

Xiaohuan Wang·Jihui Zhang

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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.

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Xiaohuan Wang, Jihui Zhang. 2019-03-20. Regularity of solutions to elliptic equations with Grushin's operator. https://arxiv.org/abs/1903.08371

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