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The singular homogeneous solutions to one phase free boundary problem


Author: Guanghao Hong
Journal: Proc. Amer. Math. Soc. 143 (2015), 4009-4015
MSC (2010): Primary 35J25, 35B65; Secondary 35J05
DOI: https://doi.org/10.1090/S0002-9939-2015-12553-1
Published electronically: March 25, 2015
MathSciNet review: 3359589
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Abstract: We provide some new examples of singular homogeneous of degree one solutions to the well-known one phase free boundary problem. They are critical points of the functional $ J(v,B)=\int _B \vert\nabla v\vert^2+\chi _{\{v>0\}}$. We also discuss their stability using a criteria of Caffarelli, Jerison and Kenig.


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Additional Information

Guanghao Hong
Affiliation: School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, People’s Republic of China 710049
Email: ghhongmath@mail.xjtu.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2015-12553-1
Keywords: Free boundary, symmetry, regularity, stability
Received by editor(s): August 24, 2013
Received by editor(s) in revised form: May 31, 2014
Published electronically: March 25, 2015
Communicated by: Tatiana Toro
Article copyright: © Copyright 2015 American Mathematical Society