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Abstract:

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.

Registro:

Documento: Artículo
Título:Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp
Autor:Acosta, G.; Armentano, M.G.; Durán, R.G.; Lombardi, A.L.
Filiación:Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, B1613GSX Provincia de Buenos Aires, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Cuspidal domains; Neumann problem; Regularity; Traces
Año:2005
Volumen:310
Número:2
Página de inicio:397
Página de fin:411
DOI: http://dx.doi.org/10.1016/j.jmaa.2005.01.065
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0022247X_v310_n2_p397_Acosta.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v310_n2_p397_Acosta

Referencias:

  • Adams, R.A., (1975) Sobolev Spaces, , New York: Academic Press
  • Grisvard, P., (1985) Elliptic Problems in Nonsmooth Domains, , Boston: Pitman
  • Grisvard, P., Problemes aux limites dans des domaines avec points de rebroussement (1995) Ann. Fac. Sci. Toulouse, 4, pp. 561-578
  • Grisvard, P., Boundary value problems in plane polygons. Instructions for use (1986) EDF Bull. Direction Études Rech. Sér. C Math. Inform., 1, pp. 21-59
  • Khelif, A., Equations aux derivees partiellles (1978) C. R. Acad. Sci. Paris, 287, pp. 1113-1116
  • Mazya, V.G., Netrusov, Yu.V., Poborchi, V., Boundary values of functions in Sobolev spaces on certain non-Lipschitzian domains (2000) St. Petersburg Math. J., 11, pp. 107-128

Citas:

---------- APA ----------
Acosta, G., Armentano, M.G., Durán, R.G. & Lombardi, A.L. (2005) . Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp. Journal of Mathematical Analysis and Applications, 310(2), 397-411.
http://dx.doi.org/10.1016/j.jmaa.2005.01.065
---------- CHICAGO ----------
Acosta, G., Armentano, M.G., Durán, R.G., Lombardi, A.L. "Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp" . Journal of Mathematical Analysis and Applications 310, no. 2 (2005) : 397-411.
http://dx.doi.org/10.1016/j.jmaa.2005.01.065
---------- MLA ----------
Acosta, G., Armentano, M.G., Durán, R.G., Lombardi, A.L. "Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp" . Journal of Mathematical Analysis and Applications, vol. 310, no. 2, 2005, pp. 397-411.
http://dx.doi.org/10.1016/j.jmaa.2005.01.065
---------- VANCOUVER ----------
Acosta, G., Armentano, M.G., Durán, R.G., Lombardi, A.L. Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp. J. Math. Anal. Appl. 2005;310(2):397-411.
http://dx.doi.org/10.1016/j.jmaa.2005.01.065