Weighted a priori estimates for elliptic equations
We give a simpler proof of the a priori estimates obtained by Durán et al. (2008, 2010) for solutions of elliptic problems in weighted Sobolev norms when the weights belong to the Muckenhoupt class A<sub>p</sub>. The argument is a generalization to bounded domains of the one used in R<...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| País: | Argentina |
| Institución: | Universidad Nacional de La Plata |
| Repositorio: | SEDICI (UNLP) |
| Idioma: | inglés |
| OAI Identifier: | oai:sedici.unlp.edu.ar:10915/98015 |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/98015 |
| Access Level: | acceso abierto |
| Palabra clave: | Matemática Ciencias Exactas Elliptic equations Weighted a priori estimates |
| Sumario: | We give a simpler proof of the a priori estimates obtained by Durán et al. (2008, 2010) for solutions of elliptic problems in weighted Sobolev norms when the weights belong to the Muckenhoupt class A<sub>p</sub>. The argument is a generalization to bounded domains of the one used in R<sup>n</sup> to prove the continuity of singular integral operators in weighted norms. In the case of singular integral operators it is known that the A<sub>p</sub> condition is also necessary for the continuity. We do not know whether this is also true for the a priori estimates in bounded domains but we are able to prove a weaker result when the operator is the Laplacian or a power of it. We prove that a necessary condition is that the weight belongs to the local A<sub>p</sub> class. |
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