Potential analysis for a class of diffusion equations: A Gaussian bounds approach
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- 作者：Ermanno Lanconelli ; Francesco Uguzzoni
- 关键词：Gaussian bounds ; Potential analysis ; Boundary behavior of PW solutions ; Non-divergence Hö ; rmander operators ; Harnack inequality
- 刊名：Journal of Differential Equations
- 出版年：2010
- 出版时间：1 May 2010
- 年：2010
- 卷：248
- 期：9
- 页码：2329-2367
- 全文大小：431 K
文摘
We axiomatically develop a potential analysis for a general class of hypoelliptic diffusion equations under the following basic assumptions: doubling condition and segment property for an underlying distance and Gaussian bounds of the fundamental solution. Our analysis is principally aimed to obtain regularity criteria and uniform boundary estimates for the Perron–Wiener solution to the Dirichlet problem. As an example of application, we also derive an exterior cone criterion of boundary regularity and scale-invariant Harnack inequality and Hölder estimate for an important class of operators in non-divergence form with Hölder continuous coefficients, modeled on Hörmander vector fields.