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Abstract:

In this paper we study asymptotics as p→ ∞ of the Dirichlet eigenvalue problem for the 1-homogeneous p -Laplacian, that is,-1/p|Du| 2-p div (|Du| p-2 Du)=λu, in Ω, u=0, on δ ωHere Ω is a bounded starshaped domain in ℝ n and p>n. There exists a principal eigenvalue λ 1,p (Ω), which is positive, and has associated a non-negative nontrivial eigenfunction. Moreover, we show that lim p → ∞ λ 1,p(Ω)= λ 1,∞(Ω), where λ 1,∞(Ω) is the first eigenvalue corresponding to the 1-homogeneous infinity Laplacian, that is, -(D 2 u Du/|Du|) ̇ D/|Du| =λ u. © 2013 Universidad Complutense de Madrid.

Registro:

Documento: Artículo
Título:The limit as p→ ∞ for the eigenvalue problem of the 1-homogeneous p -Laplacian
Autor:Martínez-Aparicio, P.J.; Pérez-Llanos, M.; Rossi, J.D.
Filiación:Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202 Murcia, Spain
Departamento de Matemáticas, Universidad Autonoma de Madrid Campus de Cantoblanco, 28049 Madrid, Spain
Departamento de Análisis Matemático, Universidad de Alicante, Ap. correos 99, 03080 Alicante, Spain
Departamento de Matemática, FCEyN, UBA Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina
Palabras clave:1-Homogeneous p-Laplacian; Infinity Laplacian
Año:2014
Volumen:27
Número:1
Página de inicio:241
Página de fin:258
DOI: http://dx.doi.org/10.1007/s13163-013-0124-4
Título revista:Revista Matematica Complutense
Título revista abreviado:Rev. Mat. Complutense
ISSN:11391138
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11391138_v27_n1_p241_MartinezAparicio

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Citas:

---------- APA ----------
Martínez-Aparicio, P.J., Pérez-Llanos, M. & Rossi, J.D. (2014) . The limit as p→ ∞ for the eigenvalue problem of the 1-homogeneous p -Laplacian. Revista Matematica Complutense, 27(1), 241-258.
http://dx.doi.org/10.1007/s13163-013-0124-4
---------- CHICAGO ----------
Martínez-Aparicio, P.J., Pérez-Llanos, M., Rossi, J.D. "The limit as p→ ∞ for the eigenvalue problem of the 1-homogeneous p -Laplacian" . Revista Matematica Complutense 27, no. 1 (2014) : 241-258.
http://dx.doi.org/10.1007/s13163-013-0124-4
---------- MLA ----------
Martínez-Aparicio, P.J., Pérez-Llanos, M., Rossi, J.D. "The limit as p→ ∞ for the eigenvalue problem of the 1-homogeneous p -Laplacian" . Revista Matematica Complutense, vol. 27, no. 1, 2014, pp. 241-258.
http://dx.doi.org/10.1007/s13163-013-0124-4
---------- VANCOUVER ----------
Martínez-Aparicio, P.J., Pérez-Llanos, M., Rossi, J.D. The limit as p→ ∞ for the eigenvalue problem of the 1-homogeneous p -Laplacian. Rev. Mat. Complutense. 2014;27(1):241-258.
http://dx.doi.org/10.1007/s13163-013-0124-4