We develop a potential theory approach for some degenerate parabolic operators in non-divergence form and with non-smooth coecients, which are modeled on smooth Hormander vector elds. We prove necessary and sucient Wiener-type tests for the regularity of boundary points. As a consequence we obtain, in particular, a conetype criterion. We also investigate the related boundary value problem and the Holder regularity at the boundary.
Tralli, G., Uguzzoni, F. (2018). On a non-smooth potential analysis for Hörmander-type operators. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 57(2), 1-20 [10.1007/s00526-018-1301-6].
On a non-smooth potential analysis for Hörmander-type operators
Tralli, Giulio;Uguzzoni, Francesco
2018
Abstract
We develop a potential theory approach for some degenerate parabolic operators in non-divergence form and with non-smooth coecients, which are modeled on smooth Hormander vector elds. We prove necessary and sucient Wiener-type tests for the regularity of boundary points. As a consequence we obtain, in particular, a conetype criterion. We also investigate the related boundary value problem and the Holder regularity at the boundary.| File | Dimensione | Formato | |
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