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.
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},
pages = {575--601},
year = {2011},
publisher = {EDP Sciences},
volume = {17},
number = {2},
doi = {10.1051/cocv/2010019},
mrnumber = {2801332},
zbl = {1219.35074},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2010019/}
}
TY - JOUR AU - Patrizi, Stefania TI - The principal eigenvalue of the $\infty $-laplacian with the Neumann boundary condition JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 575 EP - 601 VL - 17 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2010019/ DO - 10.1051/cocv/2010019 LA - en ID - COCV_2011__17_2_575_0 ER -
%0 Journal Article %A Patrizi, Stefania %T The principal eigenvalue of the $\infty $-laplacian with the Neumann boundary condition %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 575-601 %V 17 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2010019/ %R 10.1051/cocv/2010019 %G en %F 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, Tome 17 (2011) no. 2, pp. 575-601. doi: 10.1051/cocv/2010019
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