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Abstract:

In this paper we study the behaviour of the solutions to the eigenvalue problem corresponding to the p (x)-Laplacian operator{(- div (| ∇ u |p (x) - 2 ∇ u) = Λp (x) | u |p (x) - 2 u,, in Ω,; u = 0,, on ∂ Ω,) as p (x) → ∞. We consider a sequence of functions pn (x) that goes to infinity uniformly in over(Ω, -). Under adequate hypotheses on the sequence pn, namely that the limits∇ ln pn (x) → ξ (x), and frac(pn, n) (x) → q (x) exist, we prove that the corresponding eigenvalues Λpn and eigenfunctions upn verify that(Λpn)1 / n → Λ∞, upn → u∞ uniformly in over(Ω, -), where Λ∞, u∞ is a nontrivial viscosity solution of the following problem{(min {- Δ∞ u∞ - | ∇ u∞ |2 log (| ∇ u∞ |) 〈 ξ, ∇ u∞ 〉, | ∇ u∞ |q - Λ∞ u∞ q} = 0, in Ω,; u∞ = 0, on ∂ Ω .). © 2009 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:The behaviour of the p (x)-Laplacian eigenvalue problem as p (x) → ∞
Autor:Pérez-Llanos, M.; Rossi, J.D.
Filiación:Departamento de Matemáticas, U. Carlos III de Madrid, 28911 Leganés, Spain
Departamento de Matematica, Facultad de Ciencias Exactas y Naturales, U. de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Eigenvalue problems; p (x)-Laplacian; ∞-Laplacian
Año:2010
Volumen:363
Número:2
Página de inicio:502
Página de fin:511
DOI: http://dx.doi.org/10.1016/j.jmaa.2009.09.044
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_v363_n2_p502_PerezLlanos.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v363_n2_p502_PerezLlanos

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Citas:

---------- APA ----------
Pérez-Llanos, M. & Rossi, J.D. (2010) . The behaviour of the p (x)-Laplacian eigenvalue problem as p (x) → ∞. Journal of Mathematical Analysis and Applications, 363(2), 502-511.
http://dx.doi.org/10.1016/j.jmaa.2009.09.044
---------- CHICAGO ----------
Pérez-Llanos, M., Rossi, J.D. "The behaviour of the p (x)-Laplacian eigenvalue problem as p (x) → ∞" . Journal of Mathematical Analysis and Applications 363, no. 2 (2010) : 502-511.
http://dx.doi.org/10.1016/j.jmaa.2009.09.044
---------- MLA ----------
Pérez-Llanos, M., Rossi, J.D. "The behaviour of the p (x)-Laplacian eigenvalue problem as p (x) → ∞" . Journal of Mathematical Analysis and Applications, vol. 363, no. 2, 2010, pp. 502-511.
http://dx.doi.org/10.1016/j.jmaa.2009.09.044
---------- VANCOUVER ----------
Pérez-Llanos, M., Rossi, J.D. The behaviour of the p (x)-Laplacian eigenvalue problem as p (x) → ∞. J. Math. Anal. Appl. 2010;363(2):502-511.
http://dx.doi.org/10.1016/j.jmaa.2009.09.044