The principal eigenvalue of the -laplacian with the Neumann boundary condition
ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 2, p. 575-601

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.

DOI : https://doi.org/10.1051/cocv/2010019
Classification:  35J25,  35D40,  35P30,  35J60
Keywords: ∞-laplacian, Neumann boundary condition, principal eigenvalue, viscosity solutions
@article{COCV_2011__17_2_575_0,
     author = {Patrizi, Stefania},
     title = {The principal eigenvalue of the $\infty $-laplacian with the Neumann boundary condition},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {2},
     year = {2011},
     pages = {575-601},
     doi = {10.1051/cocv/2010019},
     zbl = {1219.35074},
     mrnumber = {2801332},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2011__17_2_575_0}
}
Patrizi, Stefania. The principal eigenvalue of the $\infty $-laplacian with the Neumann boundary condition. ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 2, pp. 575-601. doi : 10.1051/cocv/2010019. http://www.numdam.org/item/COCV_2011__17_2_575_0/

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