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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some remarks related to De Giorgi's conjecture


Authors: Yihong Du and Li Ma
Journal: Proc. Amer. Math. Soc. 131 (2003), 2415-2422
MSC (2000): Primary 35J15, 35J60
Published electronically: November 27, 2002
MathSciNet review: 1974639
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Abstract: For several classes of functions including the special case $f(u)=u-u^3$, we obtain boundedness and symmetry results for solutions of the problem $-\Delta u=f(u)$ defined on $R^n$. Our results complement a number of recent results related to a conjecture of De Giorgi.


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Additional Information

Yihong Du
Affiliation: School of Mathematical and Computer Sciences, University of New England, Armidale, New South Wales 2351, Australia
Email: ydu@turing.une.edu.au

Li Ma
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
Email: lma@math.tsinghua.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06867-3
PII: S 0002-9939(02)06867-3
Keywords: Elliptic equation, maximum principle, symmetry of solution
Received by editor(s): March 10, 2002
Published electronically: November 27, 2002
Additional Notes: The first author was partially supported by the Australian Academy of Science and Academia Sinica under an exchange program while part of this work was carried out. The second author was partially supported by a grant from the national 973 project of China and a scientific grant of Tsinghua University at Beijing.
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2002 American Mathematical Society