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

被引：9
作者：
Kogoj, Alessia E. [1 ]
机构：
[1] Univ Salerno, Dipartimento Ingn Informaz Ingn Elettr & Matemat, Via Giovanni Paolo 2,132, IT-84084 Fisciano, SA, Italy
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 262卷 / 03期
关键词：
Dirichlet problem; Perron-Wiener solution; Boundary behavior of Perron-Wiener solutions; Exterior cone criterion; Hypoelliptic operators; Potential theory; FUNDAMENTAL SOLUTION; HEAT-EQUATION;
D O I：
10.1016/j.jde.2016.10.018
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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.
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收藏
页码：1524 / 1539
页数：16
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