On the Dirichlet problem for hypoelliptic evolution equations: Perron-Wiener solution and a cone-type criterion

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Kogoj, Alessia E.¹ 

[1] Univ Salerno, Dipartimento Ingn Informaz Ingn Elettr & Matemat, Via Giovanni Paolo 2,132, IT-84084 Fisciano, SA, Italy

关键词: Dirichlet problem;    Perron-Wiener solution;    Boundary behavior of Perron-Wiener solutions;    Exterior cone criterion;    Hypoelliptic operators;    Potential theory;   

DOI  :  10.1016/j.jde.2016.10.018

来源: Elsevier

【 摘 要 】

We show how to apply harmonic spaces potential theory in the study of the Dirichlet problem for a general class of evolution hypoelliptic partial differential equations of second order. We construct Perron-Wiener solution and we provide a sufficient condition for the regularity of the boundary points. Our criterion extends and generalizes the classical parabolic-cone criterion for the Heat equation due to Effros and Kazdan. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free