Uniform W-1,W-p estimates for an elliptic operator with Robin boundary condition in a C-1 domain
Author
dc.contributor.author
Amrouche, C.
Author
dc.contributor.author
Conca Rosende, Carlos
Author
dc.contributor.author
Ghosh, A.
Author
dc.contributor.author
Ghosh, T.
Admission date
dc.date.accessioned
2020-05-08T23:04:54Z
Available date
dc.date.available
2020-05-08T23:04:54Z
Publication date
dc.date.issued
2020
Cita de ítem
dc.identifier.citation
Calculus of Variations and Partial Differential Equations (2020) 59: 18p.
es_ES
Identifier
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10.1007/s00526-020-1713-y
Identifier
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https://repositorio.uchile.cl/handle/2250/174622
Abstract
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We consider the Robin boundary value problem div(A del u) = div f + F in Omega, a C-1 domain, with (A del u - f) . n + alpha u = g on Gamma, where the matrix A belongs to VMO(R-3), and discover the uniform estimates on parallel to u parallel to (W1,p(Omega)), with 1 < p < infinity, independent of alpha. At the difference with the case p = 2, which is simpler, we call here the weak reverse Holder inequality. This estimates show that the solution of the Robin problem converges strongly to the solution of the Dirichlet (resp. Neumann) problem in corresponding spaces when the parameter alpha tends to infinity (resp. 0).
es_ES
Patrocinador
dc.description.sponsorship
Regional Program STIC-AmSud Project
PFBasal-001
AFBasal170001
NEMBICA-20-STIC-05