Monotonicity up to radially symmetric cores of positive solutions to nonlinear elliptic equations: local moving planes and unique continuation in a non-Lipschitz case
The authors consider solutions of the semilinear elliptic partial differential equation \[ \Delta u+f(u)=0,\quad x\in\Omega\subset\mathbb{R}^N \tag{1} \] which are nonnegative and vanishing at the boundary. The goal of the authors is to analyze the symmetry and the related monotonicity question for nonlinearities that are continuous but not Lipschitz continuous. The basic tools in the proof are a local variant of the moving plane method and the unique continuation principle.
scientific article; zbMATH DE number 2102585
scientific article