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arXiv · 1606.07133

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

Alessia E. Kogoj
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Abstract

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.

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Alessia E. Kogoj. 2016-06-22. On the Dirichlet Problem for hypoelliptic evolution equations: Perron-Wiener solution and a cone-type criterion. https://arxiv.org/abs/1606.07133

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