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

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• 作者：Alessia E. Kogoj ^{akogoj@unisa.it}
• 关键词：35H10 ; 35K70 ; 35K65 ; 31D05 ; 35D99 ; 35J25
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：1524-1539
• 全文大小：317 K
• 卷排序：262

文摘

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.