Critical points of solutions to a kind of linear elliptic equations in multiply connected domains

2018/11/12 by Deng, Haiyun, Liu, Hairong, Yang, Xiaoping
#35B38 #35J25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.04758

Abstract

In this paper, we mainly study the critical points and critical zero points of solutions u to a kind of linear elliptic equations with nonhomogeneous Dirichlet boundary conditions in a multiply connected domain Ω in ℝ². Based on the fine analysis about the distributions of connected components of the super-level sets \x∈ Ω: u(x)>t\ and sub-level sets \x∈ Ω: u(x)

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