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arXiv · 2610.07225

The Dirichlet problem with boundary data of fractional smoothness in domains with Ahlfors regular boundary

Ariel Barton·Svitlana Mayboroda·Alberto Pacati
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Abstract

We establish well posedness of the Dirichlet problem in weak local John domains $Ω\subset\R^\dmn$ with Ahlfors regular boundaries of possibly non integer dimension $0<\bdmn<\dmn$, for linear second order elliptic equations with real coefficients, and with data in Besov spaces with a very broad range of acceptable parameters.

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Ariel Barton, Svitlana Mayboroda, Alberto Pacati. 2026-10-05. The Dirichlet problem with boundary data of fractional smoothness in domains with Ahlfors regular boundary. https://arxiv.org/abs/2610.07225

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