Volume 17, Number 2, April-June 2011
|Page(s)||575 - 601|
|Published online||10 May 2010|
The principal eigenvalue of the ∞-Laplacian with the Neumann boundary condition
SAPIENZA Università di Roma, Dipartimento di Matematica,
Piazzale A. Moro 2, 00185 Roma, Italy. firstname.lastname@example.org
We prove the existence of a principal eigenvalue associated to the ∞-Laplacian plus lower order terms and the Neumann boundary condition in a bounded smooth domain. As an application we get uniqueness and existence results for the Neumann problem and a decay estimate for viscosity solutions of the Neumann evolution problem.
Mathematics Subject Classification: 35J25 / 35D40 / 35P30 / 35J60
Key words: ∞-Laplacian / Neumann boundary condition / principal eigenvalue / viscosity solutions
© EDP Sciences, SMAI, 2010
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