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: JOUR
Materias:
Cuspidal domains
Neumann problem
Regularity
Traces
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v310_n2_p397_Acosta
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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_0022247X_v310_n2_p397_Acosta2023-10-03T14:29:09Z Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp Acosta, G. Armentano, M.G. Durán, R.G. Lombardi, A.L. Cuspidal domains Neumann problem Regularity Traces 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0022247X_v310_n2_p397_Acosta
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (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 JOUR
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
url http://hdl.handle.net/20.500.12110/paper_0022247X_v310_n2_p397_Acosta
work_keys_str_mv AT acostag nonhomogeneousneumannproblemforthepoissonequationindomainswithanexternalcusp
AT armentanomg nonhomogeneousneumannproblemforthepoissonequationindomainswithanexternalcusp
AT duranrg nonhomogeneousneumannproblemforthepoissonequationindomainswithanexternalcusp
AT lombardial nonhomogeneousneumannproblemforthepoissonequationindomainswithanexternalcusp
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