Seminario Análisis y Aplicaciones
Muckenhoupt’s theory of weights applied to boundary value problems on Lipschitz graphs
Ponente: Fernando Ballesta-Yagüe (UCM)Fecha: viernes 28 de noviembre de 2025 - 11:30Lugar: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Resumen:
In the 80’s, Carlos Kenig used Muckenhoupt’s theory of weights to study the L^p Dirichlet problem for Laplace’s equation on graph Lipschitz domains in the plane. Indeed, he proved that it is solvable for every p ∈ (2 − ε, ∞), for some ε that depends on the domain. This technique involved a conformal mapping, so it was superseded by other methods that worked in higher dimensions.
However, it has been recently recovered by María J. Carro, Virginia Naibo and Carmen Ortiz-Caraballo, among other authors, to study other boundary conditions and prove L^p,1-endpoint results.
In this talk, we will focus on the Neumann and Regularity problems with A∞-weights on the boundary. These will motivate the study of a Sawyer-type inequality and the problem of extending analytically an A∞-weight defined on a Lipschitz curve.
This is joint work with María J. Carro.
