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
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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
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Palabras clave: | 1-Homogeneous p-Laplacian; Infinity Laplacian |
Año: | 2014
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Volumen: | 27
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Número: | 1
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Página de inicio: | 241
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Página de fin: | 258
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DOI: |
http://dx.doi.org/10.1007/s13163-013-0124-4 |
Título revista: | Revista Matematica Complutense
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Título revista abreviado: | Rev. Mat. Complutense
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ISSN: | 11391138
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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