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The Dirichlet problem with boundary data of fractional smoothness in domains with Ahlfors regular boundary
Abstract
We establish well posedness of the Dirichlet problem in weak local John domains Ω⊂Rdmn 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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BibTeX
@misc{barton2026dirichlet,
title = {{The Dirichlet problem with boundary data of fractional smoothness in domains with Ahlfors regular boundary}},
author = {Ariel Barton and Svitlana Mayboroda and Alberto Pacati},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07225},
eprint = {2610.07225},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07225},
}
RIS
TY - UNPB
TI - The Dirichlet problem with boundary data of fractional smoothness in domains with Ahlfors regular boundary
AU - Ariel Barton
AU - Svitlana Mayboroda
AU - Alberto Pacati
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07225
UR - https://arxiv.org/abs/2610.07225
AB - We establish well posedness of the Dirichlet problem in weak local John domains Ω⊂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.
ER -