Regularity of solutions to elliptic equations with Grushin's operator

2019/03/20 by Xiaohuan Wang, Jihui Zhang, Wang, Xiaohuan +1
Computer Science · Mathematics · #35J08 #35J70 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1903.08371

openalex publication_date 2019/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Lp estimates for the wave equation associated to the Grushin operator

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