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Abstract:

This work is devoted to the study of the elliptic equation u = f(x, u) in an exterior non-smooth domain. Applying the method of upper and lower solutions and a diagonal argument, we prove the existence of solutions under various boundary conditions. © Walter de Gruyter 2007.

Registro:

Documento: Artículo
Título:Solutions of nonlinear elliptic equations in unbounded Lipschitz domains
Autor:Amster, P.; Mariani, M.-C.; Méndez, O.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Pabellón I, (1428) Buenos Aires, Argentina
Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003-8001, United States
Department of Mathematics, 124 Bell Hall, University of Texas at El Paso, 500W University Ave., El Paso, TX 79968, United States
Año:2007
Volumen:19
Número:1
Página de inicio:115
Página de fin:125
DOI: http://dx.doi.org/10.1515/FORUM.2007.005
Título revista:Forum Mathematicum
Título revista abreviado:Forum Math.
ISSN:09337741
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09337741_v19_n1_p115_Amster

Referencias:

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  • Amrouche, C., Girault, V., Giroire, J., Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator (1997) An approach in weighted Sobolev Spaces. J. Math. Pures Appl, 76, pp. 55-81
  • Amster, P., Averbuj, C., Mariani, M.C., Solutions to a stationary nonlinear Black-Scholes type equation (2002) J. Math. Anal. Appl, 276, pp. 231-238
  • Fabes, E., Méndez, O., Mitrea, M., Boundary layers on Sobolev-Besov spaces and Poisson's equation for the Laplacian in Lipschitz domains (1998) J. Funct. Anal, 159, pp. 323-368
  • Gilbarg D., Trudinger N. S.: Elliptic Partial Differential Equations of Second Order. Springer-Verlag, 1983; Girault V.: The Divergence, Curl and Stokes Operators in Exterior Domains of K.3. Recent Developments in Theoretical Fluid Mechanics (Paseky, 1992). Pitman Res. Notes Math. Ser. 291. Longman Sci. Tech., Harlow 1993; pp 34-77; Giroire, J., Nedelec, J., Numerical Solution of an Exterior Neumann Problem Using a Double Layer Potential (1978) Math. Comp, 32, pp. 973-990
  • Grisvard, P., (1985) Elliptic problems in non-smooth domains, , Pittman advanced publishing program
  • Jerison, D., Kenig, C., The inhomogeneous Dirichlet problem in Lipschitz domains (1995) J. Funct. Anal, 130, pp. 161-219
  • Lang, J., Méndez, O., Potential techniques and regularity of boundary value problems in exterior non-smooth domains, , www.math.ohio-state.edu/~Lang/Listofpub.html, Preprint
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  • Me Owen, R., Boundary Value Problems for the Laplacian in an Exterior Domain (1981) Comm. Partial Differential Equations, 6, pp. 783-798
  • Méndez, O., Mitrea, M., Complex powers of the Laplacian in Lipschitz domains, , to appear in Math. Nachr
  • Méndez O. and Mitrea M.: The Banach envelope of Besov and Triebel-Lizorkin spaces and applications; to appear in J. Fourier Anal. Appl; Triebel, H., Spaces of Kudrjavcev Type I: Interpolation, Embedding and Structure (1976) J. Math. Anal. Appl, 56, pp. 253-277
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  • Verchota, G., Layer Potentials and regularity for the Dirichlet Problem for Laplace's Equation in Lipschitz Domains (1984) J. Funct. Anal, 59, pp. 572-611

Citas:

---------- APA ----------
Amster, P., Mariani, M.-C. & Méndez, O. (2007) . Solutions of nonlinear elliptic equations in unbounded Lipschitz domains. Forum Mathematicum, 19(1), 115-125.
http://dx.doi.org/10.1515/FORUM.2007.005
---------- CHICAGO ----------
Amster, P., Mariani, M.-C., Méndez, O. "Solutions of nonlinear elliptic equations in unbounded Lipschitz domains" . Forum Mathematicum 19, no. 1 (2007) : 115-125.
http://dx.doi.org/10.1515/FORUM.2007.005
---------- MLA ----------
Amster, P., Mariani, M.-C., Méndez, O. "Solutions of nonlinear elliptic equations in unbounded Lipschitz domains" . Forum Mathematicum, vol. 19, no. 1, 2007, pp. 115-125.
http://dx.doi.org/10.1515/FORUM.2007.005
---------- VANCOUVER ----------
Amster, P., Mariani, M.-C., Méndez, O. Solutions of nonlinear elliptic equations in unbounded Lipschitz domains. Forum Math. 2007;19(1):115-125.
http://dx.doi.org/10.1515/FORUM.2007.005