On the Dirichlet Problem for hypoelliptic evolution equations: Perron-Wiener solution and a cone-type criterion
Analysis of PDEs
2016-06-24 v1
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.
Cite
@article{arxiv.1606.07133,
title = {On the Dirichlet Problem for hypoelliptic evolution equations: Perron-Wiener solution and a cone-type criterion},
author = {Alessia E. Kogoj},
journal= {arXiv preprint arXiv:1606.07133},
year = {2016}
}