Transmission problems for simply connected domains in the complex plane

We study existence and uniqueness of a transmission problem in simply connected domains in the plane with data in weighted Lebesgue spaces by first investigating solvability results of a related novel problem associated to a homeomorphism in the real line and domains given by the upper and lower hal...

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Detalles Bibliográficos
Autores: Carro Rossell, María Jesús, Naibo, Virginia, Soria Carro, María
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/130247
Acceso en línea:https://hdl.handle.net/20.500.14352/130247
Access Level:acceso abierto
Palabra clave:Transmission problems
Graph simply connected domains
Conformal maps
Muckenhoupt weights
Matemáticas (Matemáticas)
Análisis matemático
12 Matemáticas
Descripción
Sumario:We study existence and uniqueness of a transmission problem in simply connected domains in the plane with data in weighted Lebesgue spaces by first investigating solvability results of a related novel problem associated to a homeomorphism in the real line and domains given by the upper and lower half planes. Our techniques are based on the use of conformal maps and Rellich identities for the Hilbert transform, and are motivated by previous works concerning the Dirichlet, Neumann and Zaremba problems.