Boundary value problems in graph Lipschitz domains in the plane with A∞-measures on the boundary
We prove several results for the Dirichlet, Neumann and Regularity problems for the Laplace equation in graph Lipschitz domains in the plane, considering A∞-measures on the boundary. More specifically, we study the Lp,1-solvability for the Dirichlet problem, complementing results of [25] and [10]. T...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/130362 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/130362 |
| Access Level: | acceso abierto |
| Palabra clave: | Dirichlet problem Neumann problem Regularity problem Lipschitz graph domain Lebesgue spaces Muckenhoupt weights Matemáticas (Matemáticas) Ecuaciones diferenciales 12 Matemáticas |
| Sumario: | We prove several results for the Dirichlet, Neumann and Regularity problems for the Laplace equation in graph Lipschitz domains in the plane, considering A∞-measures on the boundary. More specifically, we study the Lp,1-solvability for the Dirichlet problem, complementing results of [25] and [10]. Then, we study Lp-solvability of the Neumann problem, obtaining a range of solvability which is empty in some cases, a clear difference with the arc-length case. When it is not empty, it is an interval, and we consider solvability at its endpoints, establishing conditions for Lorentz space solvability when p>1and atomic Hardy space solvability when p =1. Solving the Lorentz endpoint leads us to a two-weight Sawyer-type inequality, for which we give a sufficient condition. Finally, we show how to adapt to the Regularity problem the results for the Neumann problem. |
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