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arXiv · 2506.14639

The Poisson-Dirichlet problem in domains with Ahlfors regular boundary

Ariel Barton·Svitlana Mayboroda·Alberto Pacati
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Abstract

We present an announcement of some recent results concerning well-posedness of the Poisson-Dirichlet problem with boundary data in Besov spaces with fractional smoothness. This is a far-reaching generalization as previously known theorems concerning well-posedness of the Poisson problem in such intermediate smoothness classes were mostly restricted to the context of Lipschitz domains and coefficients satisfying strong regularity assumptions.

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Ariel Barton, Svitlana Mayboroda, Alberto Pacati. 2025-06-17. The Poisson-Dirichlet problem in domains with Ahlfors regular boundary. https://arxiv.org/abs/2506.14639

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