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.
On the Dirichlet problem for hypoelliptic evolution equations: Perron–Wiener solution and a cone-type criterion
KOGOJ, ALESSIA ELISABETTA
Writing – Review & Editing
2017
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.File in questo prodotto:
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cone_criterion.pdf
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criterio_cono_arXiv.pdf
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