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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.07225

Authors: Barton, Ariel, Mayboroda, Svitlana, Pacati, Alberto

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: RAISE-TAQS: The Hidden Structure of the Disorder in Quantum Systems

OpenAlex ID: W7221002657

Cites: 2

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Related to: 10