Document Type
Article
Abstract
We study the asymptotic behavior as p → ∞ of the Gelfand problem
−Δpu = λeu in Ω ⊂ Rn, u = 0 on ∂Ω.
Under an appropriate rescaling on u and λ, we prove uniform convergence of solutions of the Gelfand problem to solutions of
min{|∇u|−Λeu, −Δ∞u} = 0 in Ω, u = 0 on ∂Ω.
We discuss existence, non-existence, and multiplicity of solutions of the limit problem in terms of Λ.
Disciplines
Non-linear Dynamics | Partial Differential Equations
Recommended Citation
F. Charro, B. J. Son, P. Y. Wang, The Gelfand problem for the infinity Laplacian, Math. in Engin., 5 (2023), 1-28. http://doi.org/10.3934/mine.2023022
COinS
Comments
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)