Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp
- Autores
- Acosta, G.; Armentano, M.G.; Durán, R.G.; Lombardi, A.L.
- Año de publicación
- 2005
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this work we analyze the existence and regularity of the solution of a nonhomogeneous Neumann problem for the Poisson equation in a plane domain Ω with an external cusp. In order to prove that there exists a unique solution in H1 (Ω) using the Lax-Milgram theorem we need to apply a trace theorem. Since Ω is not a Lipschitz domain, the standard trace theorem for H1 (Ω) does not apply, in fact the restriction of H1 (Ω) functions is not necessarily in L2 (∂Ω). So, we introduce a trace theorem by using weighted Sobolev norms in Ω. Under appropriate assumptions we prove that the solution of our problem is in H2 (Ω) and we obtain an a priori estimate for the second derivatives of the solution. © 2005 Elsevier Inc. All rights reserved.
Fil:Acosta, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Armentano, M.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Lombardi, A.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. - Fuente
- J. Math. Anal. Appl. 2005;310(2):397-411
- Materia
-
Cuspidal domains
Neumann problem
Regularity
Traces - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by/2.5/ar
- Repositorio
- Institución
- Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
- OAI Identificador
- paperaa:paper_0022247X_v310_n2_p397_Acosta
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Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cuspAcosta, G.Armentano, M.G.Durán, R.G.Lombardi, A.L.Cuspidal domainsNeumann problemRegularityTracesIn this work we analyze the existence and regularity of the solution of a nonhomogeneous Neumann problem for the Poisson equation in a plane domain Ω with an external cusp. In order to prove that there exists a unique solution in H1 (Ω) using the Lax-Milgram theorem we need to apply a trace theorem. Since Ω is not a Lipschitz domain, the standard trace theorem for H1 (Ω) does not apply, in fact the restriction of H1 (Ω) functions is not necessarily in L2 (∂Ω). So, we introduce a trace theorem by using weighted Sobolev norms in Ω. Under appropriate assumptions we prove that the solution of our problem is in H2 (Ω) and we obtain an a priori estimate for the second derivatives of the solution. © 2005 Elsevier Inc. All rights reserved.Fil:Acosta, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Armentano, M.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Lombardi, A.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2005info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_0022247X_v310_n2_p397_AcostaJ. Math. Anal. Appl. 2005;310(2):397-411reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-09-29T13:43:05Zpaperaa:paper_0022247X_v310_n2_p397_AcostaInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-09-29 13:43:06.994Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse |
dc.title.none.fl_str_mv |
Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp |
title |
Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp |
spellingShingle |
Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp Acosta, G. Cuspidal domains Neumann problem Regularity Traces |
title_short |
Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp |
title_full |
Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp |
title_fullStr |
Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp |
title_full_unstemmed |
Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp |
title_sort |
Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp |
dc.creator.none.fl_str_mv |
Acosta, G. Armentano, M.G. Durán, R.G. Lombardi, A.L. |
author |
Acosta, G. |
author_facet |
Acosta, G. Armentano, M.G. Durán, R.G. Lombardi, A.L. |
author_role |
author |
author2 |
Armentano, M.G. Durán, R.G. Lombardi, A.L. |
author2_role |
author author author |
dc.subject.none.fl_str_mv |
Cuspidal domains Neumann problem Regularity Traces |
topic |
Cuspidal domains Neumann problem Regularity Traces |
dc.description.none.fl_txt_mv |
In this work we analyze the existence and regularity of the solution of a nonhomogeneous Neumann problem for the Poisson equation in a plane domain Ω with an external cusp. In order to prove that there exists a unique solution in H1 (Ω) using the Lax-Milgram theorem we need to apply a trace theorem. Since Ω is not a Lipschitz domain, the standard trace theorem for H1 (Ω) does not apply, in fact the restriction of H1 (Ω) functions is not necessarily in L2 (∂Ω). So, we introduce a trace theorem by using weighted Sobolev norms in Ω. Under appropriate assumptions we prove that the solution of our problem is in H2 (Ω) and we obtain an a priori estimate for the second derivatives of the solution. © 2005 Elsevier Inc. All rights reserved. Fil:Acosta, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Armentano, M.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Lombardi, A.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. |
description |
In this work we analyze the existence and regularity of the solution of a nonhomogeneous Neumann problem for the Poisson equation in a plane domain Ω with an external cusp. In order to prove that there exists a unique solution in H1 (Ω) using the Lax-Milgram theorem we need to apply a trace theorem. Since Ω is not a Lipschitz domain, the standard trace theorem for H1 (Ω) does not apply, in fact the restriction of H1 (Ω) functions is not necessarily in L2 (∂Ω). So, we introduce a trace theorem by using weighted Sobolev norms in Ω. Under appropriate assumptions we prove that the solution of our problem is in H2 (Ω) and we obtain an a priori estimate for the second derivatives of the solution. © 2005 Elsevier Inc. All rights reserved. |
publishDate |
2005 |
dc.date.none.fl_str_mv |
2005 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/20.500.12110/paper_0022247X_v310_n2_p397_Acosta |
url |
http://hdl.handle.net/20.500.12110/paper_0022247X_v310_n2_p397_Acosta |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
http://creativecommons.org/licenses/by/2.5/ar |
dc.format.none.fl_str_mv |
application/pdf |
dc.source.none.fl_str_mv |
J. Math. Anal. Appl. 2005;310(2):397-411 reponame:Biblioteca Digital (UBA-FCEN) instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales instacron:UBA-FCEN |
reponame_str |
Biblioteca Digital (UBA-FCEN) |
collection |
Biblioteca Digital (UBA-FCEN) |
instname_str |
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
instacron_str |
UBA-FCEN |
institution |
UBA-FCEN |
repository.name.fl_str_mv |
Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
repository.mail.fl_str_mv |
ana@bl.fcen.uba.ar |
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