A symmetry result for an elliptic problem arising from the 2-D thin film equation
Ka Luen Cheung, Kai-Seng Chou · Proceedings of the American Mathematical Society · 2016
It is shown that every positive, stable $H^2_0$-solution to $\Delta u+f(u)=c$ in $\mathbb {R}^2$ is radially symmetric. This problem arises from the study of the steady states for the two dimensional thin film equation.