Critical points of solutions to a quasilinear elliptic equation with nonhomogeneous Dirichlet boundary conditions

In this paper, we mainly investigate the critical points associated to solutions u of a quasilinear elliptic equation with nonhomogeneous Dirichlet boundary conditions in a connected domain Ω in R2. Based on the fine analysis about the distribution of connected components of a super-level set {x∈Ω:u(x)>t} for any min∂Ωu(x)