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.
The Dirichlet problem for a family of totally degenerate differential operators / Manfredini, Maria; Piccinini, Mirco; Polidoro, Sergio. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - 25:3(2025), pp. 1-40. [10.1007/s00028-025-01116-3]
The Dirichlet problem for a family of totally degenerate differential operators
Manfredini, MariaMembro del Collaboration Group
;Polidoro, SergioMembro del Collaboration Group
2025
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.
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