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 Ap. The argument is a generalization to bounded domains of the one used in Rn to prove the continuity...
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2018
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v243_n1_p13_Cejas http://hdl.handle.net/20.500.12110/paper_00393223_v243_n1_p13_Cejas |
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| 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 Ap. The argument is a generalization to bounded domains of the one used in Rn to prove the continuity of singular integral operators in weighted norms. In the case of singular integral operators it is known that the Ap 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 Ap class. © 2018 Instytut Matematyczny PAN. |
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