@article{Charro2023, 
author = {Fernando Charro and Byungjae Son and Peiyong Wang},
title = {The Gelfand problem for the Infinity Laplacian},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {2},
pages = {1-28},
keywords = {fully nonlinear, infinity Laplacian, Gelfand problem},
url = {https://www.sciopen.com/article/10.3934/mine.2023022},
doi = {10.3934/mine.2023022},
abstract = {We study the asymptotic behavior as    p  →  ∞ of the Gelfand problem         {                            −                                      Δ                          p                                u          =          λ                                e                          u                                                        in                    Ω          ⊂                                    R                        n                                                        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                              |                            −              Λ                                            e                                  u                                            ,              −                              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.}
}