Some remarks related to De Giorgi’s conjecture
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- by Yihong Du and Li Ma PDF
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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.References
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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
- MR Author ID: 293769
- Email: lma@math.tsinghua.edu.cn
- 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
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1974639