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Abstract:

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.

Registro:

Documento: Artículo
Título:Weighted a priori estimates for elliptic equations
Autor:Cejas, M.E.; Durán, R.G.
Filiación:Departamento de Matemática Facultad de Ciencias Exactas, Universidad Nacional de La Plata, CONICET, Calle 50 y 115, La Plata Buenos Aires, 1900, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, IMAS-CONICET-UBA, Pabellón I, Ciudad Universitaria, CABA, 1428, Argentina
Palabras clave:Elliptic equations; Weighted a priori estimates
Año:2018
Volumen:243
Número:1
Página de inicio:13
Página de fin:24
DOI: http://dx.doi.org/10.4064/sm8704-6-2017
Título revista:Studia Mathematica
Título revista abreviado:Stud. Math.
ISSN:00393223
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v243_n1_p13_Cejas

Referencias:

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Citas:

---------- APA ----------
Cejas, M.E. & Durán, R.G. (2018) . Weighted a priori estimates for elliptic equations. Studia Mathematica, 243(1), 13-24.
http://dx.doi.org/10.4064/sm8704-6-2017
---------- CHICAGO ----------
Cejas, M.E., Durán, R.G. "Weighted a priori estimates for elliptic equations" . Studia Mathematica 243, no. 1 (2018) : 13-24.
http://dx.doi.org/10.4064/sm8704-6-2017
---------- MLA ----------
Cejas, M.E., Durán, R.G. "Weighted a priori estimates for elliptic equations" . Studia Mathematica, vol. 243, no. 1, 2018, pp. 13-24.
http://dx.doi.org/10.4064/sm8704-6-2017
---------- VANCOUVER ----------
Cejas, M.E., Durán, R.G. Weighted a priori estimates for elliptic equations. Stud. Math. 2018;243(1):13-24.
http://dx.doi.org/10.4064/sm8704-6-2017