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...
| Authors: | , , |
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| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2019 |
| Country: | España |
| Institution: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repository: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/192839 |
| Online Access: | http://hdl.handle.net/10261/192839 |
| Access Level: | Open access |
| Keyword: | 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 |
| Summary: | 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. |
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