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


Authors: Ka-Luen Cheung and Kai-Seng Chou
Journal: Proc. Amer. Math. Soc. 145 (2017), 853-860
MSC (2010): Primary 76A20; Secondary 35B35, 35K55
DOI: https://doi.org/10.1090/proc/13237
Published electronically: July 28, 2016
MathSciNet review: 3577884
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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.


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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
Email: kaluen@.eduhk.hk

Kai-Seng Chou
Affiliation: Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
Email: kschou@math.cuhk.edu.hk

DOI: https://doi.org/10.1090/proc/13237
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
Article copyright: © Copyright 2016 American Mathematical Society