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Abstract:

We study the limit as p → ∞ of the first non-zero eigenvalue of the p-Laplacian with Neumann boundary conditions in a smooth bounded domain U We prove that = 2=diam(U), where diam(U) denotes the diameter of U with respect to the geodesic distance in U. We can think of as the first eigenvalue of the Laplacian with Neumann boundary conditions. We also study the regularity of as a function of the domain U proving that under a smooth perturbation Ut of U by diffeomorphisms close to the identity there holds that (U)+O(t). Although (Ut) is in general not differentiable at t = 0, we show that in some cases it is so with an explicit formula for the derivative. © 2016 University of Houston.

Registro:

Documento: Artículo
Título:On the first nontrivial eigenvalue of the ∞-laplacian with neumann boundary conditions
Autor:Rossi, J.D.; Saintier, N.
Filiación:CONICET, Dep. de Matematica, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina
Dep. de Matematica, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina
Instituto de Ciencias, Univ. Nac. Gral Sarmiento, J. M. Gutierrez 1150, Los Polvorines-Pcia de Bs. As, C.P. 1613, Argentina
Palabras clave:Eigenvalue problems; First variations; Infinity Laplacian
Año:2016
Volumen:42
Número:2
Página de inicio:613
Página de fin:635
Título revista:Houston Journal of Mathematics
Título revista abreviado:Houst. J. Math.
ISSN:03621588
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03621588_v42_n2_p613_Rossi

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Citas:

---------- APA ----------
Rossi, J.D. & Saintier, N. (2016) . On the first nontrivial eigenvalue of the ∞-laplacian with neumann boundary conditions. Houston Journal of Mathematics, 42(2), 613-635.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03621588_v42_n2_p613_Rossi [ ]
---------- CHICAGO ----------
Rossi, J.D., Saintier, N. "On the first nontrivial eigenvalue of the ∞-laplacian with neumann boundary conditions" . Houston Journal of Mathematics 42, no. 2 (2016) : 613-635.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03621588_v42_n2_p613_Rossi [ ]
---------- MLA ----------
Rossi, J.D., Saintier, N. "On the first nontrivial eigenvalue of the ∞-laplacian with neumann boundary conditions" . Houston Journal of Mathematics, vol. 42, no. 2, 2016, pp. 613-635.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03621588_v42_n2_p613_Rossi [ ]
---------- VANCOUVER ----------
Rossi, J.D., Saintier, N. On the first nontrivial eigenvalue of the ∞-laplacian with neumann boundary conditions. Houst. J. Math. 2016;42(2):613-635.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03621588_v42_n2_p613_Rossi [ ]