@article{Choi2023, 
author = {Woocheol Choi},
title = {Energy minimizing solutions to slightly subcritical elliptic problems on nonconvex polygonal domains},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {26134-26152},
keywords = {blow-up analysis, polygonal domains, Lane-Emden-Fowler equation},
url = {https://www.sciopen.com/article/10.3934/math.20231332},
doi = {10.3934/math.20231332},
abstract = {In this paper we are concerned with the Lane-Emden-Fowler equation         {                            −          Δ          u                          =                      u                                                            n                  +                  2                                                  n                  −                  2                                            −              ε                                                                          i              n                                          Ω          ,                                      u                          >          0                                                    i              n                                          Ω          ,                                      u                          =          0                                                    o              n                                          ∂          Ω          ,                        where    Ω  ⊂            R        n   (   n  ≥  3) is a nonconvex polygonal domain and    ε  >  0. We study the asymptotic behavior of minimal energy solutions as    ε  >  0 goes to zero. A main part is to show that the solution is uniformly bounded near the boundary with respect to    ε  >  0. The moving plane method is difficult to apply for the nonconvex polygonal domain. To get around this difficulty, we derive a contradiction after assuming that the solution blows up near the boundary by using the Pohozaev identity and the Green's function.}
}