A symmetry result for an elliptic problem arising from the 2-D thin film equation
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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.References
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Additional Information
- Ka-Luen Cheung
- Affiliation: Department of Mathematics and Information Technology, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong
- MR Author ID: 718599
- Email: kaluen@.eduhk.hk
- Kai-Seng Chou
- Affiliation: Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
- MR Author ID: 223998
- Email: kschou@math.cuhk.edu.hk
- Received by editor(s): January 23, 2016
- Received by editor(s) in revised form: April 9, 2016
- Published electronically: July 28, 2016
- Communicated by: Joachim Krieger
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 853-860
- MSC (2010): Primary 76A20; Secondary 35B35, 35K55
- DOI: https://doi.org/10.1090/proc/13237
- MathSciNet review: 3577884