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

En:

J. Math. Anal. Appl. 2005;310(2):397-411

Fecha:

2005

Formato:

application/pdf

Tipo de documento:

info:eu-repo/semantics/article
info:ar-repo/semantics/artículo
info:eu-repo/semantics/publishedVersion

Descriptores:

Cuspidal domains -  Neumann problem -  Regularity -  Traces

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.

Identificador(es):

http://hdl.handle.net/20.500.12110/paper_0022247X_v310_n2_p397_Acosta

Derechos:

info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar