Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp

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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....

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Autores principales:	Acosta, G., Armentano, M.G., Durán, R.G., Lombardi, A.L.
Formato:	Artículo publishedVersion
Publicado:	2005
Materias:	Cuspidal domains Neumann problem Regularity Traces
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_0022247X_v310_n2_p397_Acosta https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v310_n2_p397_Acosta_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

id	I28-R145-paper_0022247X_v310_n2_p397_Acosta_oai
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spelling	I28-R145-paper_0022247X_v310_n2_p397_Acosta_oai2024-08-16 Acosta, G. Armentano, M.G. Durán, R.G. Lombardi, A.L. 2005 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. application/pdf http://hdl.handle.net/20.500.12110/paper_0022247X_v310_n2_p397_Acosta info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Math. Anal. Appl. 2005;310(2):397-411 Cuspidal domains Neumann problem Regularity Traces Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v310_n2_p397_Acosta_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
topic	Cuspidal domains Neumann problem Regularity Traces
spellingShingle	Cuspidal domains Neumann problem Regularity Traces Acosta, G. Armentano, M.G. Durán, R.G. Lombardi, A.L. Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp
topic_facet	Cuspidal domains Neumann problem Regularity Traces
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.
format	Artículo Artículo publishedVersion
author	Acosta, G. Armentano, M.G. Durán, R.G. Lombardi, A.L.
author_facet	Acosta, G. Armentano, M.G. Durán, R.G. Lombardi, A.L.
author_sort	Acosta, G.
title	Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp
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
publishDate	2005
url	http://hdl.handle.net/20.500.12110/paper_0022247X_v310_n2_p397_Acosta https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v310_n2_p397_Acosta_oai
work_keys_str_mv	AT acostag nonhomogeneousneumannproblemforthepoissonequationindomainswithanexternalcusp AT armentanomg nonhomogeneousneumannproblemforthepoissonequationindomainswithanexternalcusp AT duranrg nonhomogeneousneumannproblemforthepoissonequationindomainswithanexternalcusp AT lombardial nonhomogeneousneumannproblemforthepoissonequationindomainswithanexternalcusp
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Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp

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