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Abstract:

In this paper we study the dependence of the first eigenvalue of the infinity Laplace with respect to the domain. We prove that this first eigenvalue is continuous under some weak convergence conditions which are fulfilled when a sequence of domains converges in Hausdorff distance. Moreover, it is Lipschitz continuous but not differentiable when we consider deformations obtained via a vector field. Our results are illustrated with simple examples. © Glasgow Mathematical Journal Trust 2013.

Registro:

Documento: Artículo
Título:The dependence of the first eigenvalue of the infinity laplacian with respect to the domain
Autor:Navarro, J.C.; Rossi, J.D.; San Antolin, A.; Saintier, N.
Filiación:Departamento de Análisis Matemático, Universidad de Alicante, Ap. Correos 99, 03080 Alicante, Spain
Departamento de Matemática, FCEyN Universidad de Buenos Aires (1428) Buenos Aires, Instituto de Ciencias - Universidad Nacional de General Sarmiento, J. M. Gutierrez 1150, C.P. 1613 Los Polvorines, Pcia de Bs. As., Argentina
Año:2014
Volumen:56
Número:2
Página de inicio:241
Página de fin:249
DOI: http://dx.doi.org/10.1017/S0017089513000219
Título revista:Glasgow Mathematical Journal
Título revista abreviado:Glasgow. Math. J.
ISSN:00170895
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00170895_v56_n2_p241_Navarro

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Citas:

---------- APA ----------
Navarro, J.C., Rossi, J.D., San Antolin, A. & Saintier, N. (2014) . The dependence of the first eigenvalue of the infinity laplacian with respect to the domain. Glasgow Mathematical Journal, 56(2), 241-249.
http://dx.doi.org/10.1017/S0017089513000219
---------- CHICAGO ----------
Navarro, J.C., Rossi, J.D., San Antolin, A., Saintier, N. "The dependence of the first eigenvalue of the infinity laplacian with respect to the domain" . Glasgow Mathematical Journal 56, no. 2 (2014) : 241-249.
http://dx.doi.org/10.1017/S0017089513000219
---------- MLA ----------
Navarro, J.C., Rossi, J.D., San Antolin, A., Saintier, N. "The dependence of the first eigenvalue of the infinity laplacian with respect to the domain" . Glasgow Mathematical Journal, vol. 56, no. 2, 2014, pp. 241-249.
http://dx.doi.org/10.1017/S0017089513000219
---------- VANCOUVER ----------
Navarro, J.C., Rossi, J.D., San Antolin, A., Saintier, N. The dependence of the first eigenvalue of the infinity laplacian with respect to the domain. Glasgow. Math. J. 2014;56(2):241-249.
http://dx.doi.org/10.1017/S0017089513000219