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The principal eigenvalue of the ∞-Laplacian with the Neumann boundary condition

Published online by Cambridge University Press:  10 May 2010

Stefania Patrizi
Stefania Patrizi*
Affiliation:
SAPIENZA Università di Roma, Dipartimento di Matematica, Piazzale A. Moro 2, 00185 Roma, Italy. patrizi@mat.uniroma1.it
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Abstract

We prove the existence of a principal eigenvalue associated to the∞-Laplacian plus lower order terms and the Neumann boundarycondition in a bounded smooth domain. As an application we getuniqueness and existence results for the Neumann problem and adecay estimate for viscosity solutions of the Neumann evolutionproblem.

Keywords

∞-LaplacianNeumann boundary conditionprincipal eigenvalueviscosity solutions
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 2 , April 2011 , pp. 575 - 601
Copyright
© EDP Sciences, SMAI, 2010

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