In the framework of Potential Theory we prove existence for the Perron-Weiner-Brelot-Bauer solution to the Dirichlet problem related to a family of totally degenerate, in the sense of Bony, differential operators. We also state and prove a Wiener-type criterium and an exterior cone condition for the regularity of a boundary point. Our results apply to a wide family of strongly degenerate operators that includes the following example L=t2Δx+⟨x,∇y⟩-∂t, for (x,y,t)∈RN×RN×R.
The Dirichlet problem for a family of totally degenerate differential operators
Piccinini, Mirco;
2025-01-01
Abstract
In the framework of Potential Theory we prove existence for the Perron-Weiner-Brelot-Bauer solution to the Dirichlet problem related to a family of totally degenerate, in the sense of Bony, differential operators. We also state and prove a Wiener-type criterium and an exterior cone condition for the regularity of a boundary point. Our results apply to a wide family of strongly degenerate operators that includes the following example L=t2Δx+⟨x,∇y⟩-∂t, for (x,y,t)∈RN×RN×R.File in questo prodotto:
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