The dependence of the first eigenvalue of the infinity Laplacian with respect to the domain
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Title: | The dependence of the first eigenvalue of the infinity Laplacian with respect to the domain |
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Authors: | Navarro Climent, José Carlos | Rossi, Julio D. | San Antolín Gil, Ángel | Saintier, Nicolas |
Research Group/s: | Curvas Alpha-Densas. Análisis y Geometría Local |
Center, Department or Service: | Universidad de Alicante. Departamento de Análisis Matemático |
Keywords: | Nonlinear elliptic equations | Eigenvalues |
Knowledge Area: | Análisis Matemático |
Issue Date: | 2-Sep-2013 |
Publisher: | Cambridge University Press |
Citation: | Glasgow Mathematical Journal. 2014, 56(2): 241-249. doi:10.1017/S0017089513000219 |
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. |
Sponsor: | Partially supported by MEC MTM2010-18128 (Spain). |
URI: | http://hdl.handle.net/10045/36560 |
ISSN: | 0017-0895 (Print) | 1469-509X (Online) |
DOI: | 10.1017/S0017089513000219 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © Glasgow Mathematical Journal Trust 2013 |
Peer Review: | si |
Publisher version: | http://dx.doi.org/10.1017/S0017089513000219 |
Appears in Collections: | INV - CADAGL - Artículos de Revistas INV - GAM - Artículos de Revistas |
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2014_Navarro_etal_Glasgow-Math-J.pdf | 76,45 kB | Adobe PDF | Open Preview | |
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