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

DOI:
https://doi.org/10.1090/S0002-9939-02-06867-3

Published electronically:
November 27, 2002

MathSciNet review:
1974639

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Abstract | References | Similar Articles | Additional Information

Abstract: For several classes of functions including the special case , we obtain boundedness and symmetry results for solutions of the problem defined on . 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:
https://doi.org/10.1090/S0002-9939-02-06867-3

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