@article{Li2022, 
author = {Keqiang Li and Shangjiu Wang and Shaoyong Li},
title = {Symmetry of large solutions for semilinear elliptic equations in a symmetric convex domain},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {6},
pages = {10860-10866},
keywords = {semilinear elliptic systems, moving plane method, maximum principle, symmetry of large solutions},
url = {https://www.sciopen.com/article/10.3934/math.2022607},
doi = {10.3934/math.2022607},
abstract = {In this paper, we consider the solutions of the boundary blow-up problem                                 {                                                    Δ                u                =                                  1                                      u                    γ                                                  +                f                (                u                )                                                                                                  i                  n                                                                                Ω                ,                                                                                    u                >                0                                                                                                                                                                                                                                                                                                                                                                                  i                  n                                                                                Ω                ,                                                                                    u                =                +                ∞                                                                                                                                                                                                                                                                                  o                  n                                                                ∂                Ω                ,                                                                  where    γ  >  0  ,    Ω is a bounded convex smooth domain and symmetric w.r.t. a direction.    f is a locally Lipschitz continuous and non-decreasing function. We prove symmetry and monotonicity of solutions of the problem above by the moving planes method. A maximum principle in narrow domains plays an important role in proof of the main result.}
}