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<...
Guardado en:
| Autores principales: | , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2018
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/98015 https://ri.conicet.gov.ar/11336/84701 http://www.impan.pl/get/doi/10.4064/sm8704-6-2017 |
| Aporte de: |
| 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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