Optimal Regularity of a Degenerate Elliptic Equation

Author:

Wang XiaohuanORCID,Zhang Jihui

Abstract

AbstractIn this paper, we consider the optimal regularity of solutions to elliptic equation with a Grushin-like 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-like operator is a degenerate operator.

Funder

National Natural Science Foundation of China

Publisher

Springer Science and Business Media LLC

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Reference24 articles.

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4. Di Fazio, G., Fanciullo, M., Zamboni, P.: Regularity for a class of strongly degenerate quasilinear operators. J. Differ. Equ. 255, 3920–3939 (2013)

5. Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order, 2nd edn. Springer, New York (1983)

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