A symmetry result for an elliptic problem arising from the 2-D thin film equation

Cheung, Ka-Luen; Chou, Kai-Seng

doi:10.1090/proc/13237

A symmetry result for an elliptic problem arising from the 2-D thin film equation
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Proc. Amer. Math. Soc. 145 (2017), 853-860 Request permission

Abstract:

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.

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