抛物型Baouendi-Grushin Laplace方程解的Schauder估计
Schauder Estimates for Parabolic Baouendi-Grushin Laplace Equations
DOI: 10.12677/PM.2020.1012146, PDF,    科研立项经费支持
作者: 元 琛, 黄小涛：南京航空航天大学，江苏 南京
关键词: 退化抛物方程；Baouendi-Grushin算子；Schauder估计；Degenerate Parabolic Equations； Baouendi-Grushin Operator； Schauder Estimates
摘要: 本文研究了一类退化抛物Baouendi-Grushin Laplace方程。通过构造与Baouemdi-Grushin向量场相对应的抛物Carnot-Carathéodory度量，利用嵌入定理和紧方法来证明方程解的Schauder估计。
Abstract: In this paper, we investigate a class of degenerate parabolic Baouendi-Grushin Laplace equations. By introducing the parabolic Carnot-Caratheodory metric which is associated with the geometry of the Baouendi-Grushin vector fields, we use imbedding theorem and compactness method to prove the Schauder estimates for the solutions of parabolic Baouendi-Grushin Laplace equations.
文章引用：元琛, 黄小涛. 抛物型Baouendi-Grushin Laplace方程解的Schauder估计[J]. 理论数学, 2020, 10(12): 1229-1239. https://doi.org/10.12677/PM.2020.1012146

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