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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Autores principales: Cejas, M.E., Durán, R.G.
Formato: JOUR
Materias:
Elliptic equations
Weighted a priori estimates
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00393223_v243_n1_p13_Cejas
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00393223_v243_n1_p13_Cejas2023-10-03T14:49:48Z Weighted a priori estimates for elliptic equations Cejas, M.E. Durán, R.G. Elliptic equations Weighted a priori estimates 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00393223_v243_n1_p13_Cejas
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Elliptic equations
Weighted a priori estimates
spellingShingle Elliptic equations
Weighted a priori estimates
Cejas, M.E.
Durán, R.G.
Weighted a priori estimates for elliptic equations
topic_facet Elliptic equations
Weighted a priori estimates
description 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.
format JOUR
author Cejas, M.E.
Durán, R.G.
author_facet Cejas, M.E.
Durán, R.G.
author_sort Cejas, M.E.
title Weighted a priori estimates for elliptic equations
title_short Weighted a priori estimates for elliptic equations
title_full Weighted a priori estimates for elliptic equations
title_fullStr Weighted a priori estimates for elliptic equations
title_full_unstemmed Weighted a priori estimates for elliptic equations
title_sort weighted a priori estimates for elliptic equations
url http://hdl.handle.net/20.500.12110/paper_00393223_v243_n1_p13_Cejas
work_keys_str_mv AT cejasme weightedaprioriestimatesforellipticequations
AT duranrg weightedaprioriestimatesforellipticequations
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