The generalized Hölder and Morrey-Campanato Dirichlet problems for elliptic systems in the upper-half space

We prove well-posedness results for the Dirichlet problem in Rn + for homogeneous, second order, constant complex coe cient elliptic systems with boundary data in generalized H older spaces C !(Rn1;CM) and in generalized Morrey-Campanato spaces E !;p(Rn1;CM) under certain assumptions on the growth f...

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Detalles Bibliográficos
Autores: Marín, Juan José, Martell, José María, Mitrea, Marius
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/192839
Acceso en línea:http://hdl.handle.net/10261/192839
Access Level:acceso abierto
Palabra clave:Generalized H older space
Generalized Morrey-Campanato space
Dirichlet problem in the upper-half space
Second order elliptic system
Poisson kernel
Lamé system
Nontangential pointwise trace
Fatou type theorem
Descripción
Sumario:We prove well-posedness results for the Dirichlet problem in Rn + for homogeneous, second order, constant complex coe cient elliptic systems with boundary data in generalized H older spaces C !(Rn1;CM) and in generalized Morrey-Campanato spaces E !;p(Rn1;CM) under certain assumptions on the growth function !. We also identify a class of growth functions ! for which C !(Rn1;CM) = E !;p(Rn1;CM) and for which the aforementioned well-posedness results are equivalent, in the sense that they have the same unique solution, satisfying natural regularity properties and estimates.