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Symmetry of integral equations on bounded domains
Author(s):
Dongsheng
Li;
Gerhard
Ströhmer;
Lihe
Wang
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3695-3702.
MSC (2000):
Primary 45K05, 45P05;
Secondary 35J67
Posted:
June 12, 2009
MathSciNet review:
2529876
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Abstract:
In this paper, we will investigate the symmetry of both domains and solutions of integral equations on bounded domains via the method of moving planes.
References:
-
- 1.
- W.X. Chen, C.M. Li and B. Ou, Classification of solutions for an integral equation, Comm. Pure and Appl. Math. LIX (2006), 330-343. MR 2200258 (2006m:45007a)
- 2.
- B. Gidas, W. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209-243. MR 544879 (80h:35043)
- 3.
- J. Serrin, A symmetry problem in potential theory, Arch. Rat. Mech. Anal. 43 (1971), 304-318. MR 0333220 (48:11545)
- 4.
- G. Ströhmer, About the linear stability of the spherically symmetric solution for the equations of a barotropic viscous fluid under the influence of self-gravitation, J. Math. Fluid Mech. 8 (2006), 36-63. MR 2205150 (2006i:76089)
- 5.
- G. Ströhmer and W. Zajaczkowski, On the existence and properties of the rotationally symmetric equilibrium states of compressible barotropic self-gravitating fluids, Indiana Univ. Math. J. 46 (1997), 1181-1220. MR 1631576 (99g:76124)
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Additional Information:
Dongsheng
Li
Affiliation:
College of Science, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
Email:
lidsh@mail.xjtu.edu.cn
Gerhard
Ströhmer
Affiliation:
Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242-1419
Email:
strohmer@math.uiowa.edu
Lihe
Wang
Affiliation:
Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242-1419
Email:
lwang@math.uiowa.edu
DOI:
10.1090/S0002-9939-09-09987-0
PII:
S 0002-9939(09)09987-0
Keywords:
Symmetry,
integral equations,
moving planes
Received by editor(s):
August 13, 2008
Posted:
June 12, 2009
Additional Notes:
The first author was supported in part by NSF of China Grant #10771166.
The second author was supported in part by PCSR Grant #2 PO3A 002223.
The third author was supported in part by NSF Grant # DMS-0701392.
Communicated by:
Matthew J. Gursky
Copyright of article:
Copyright
2009,
American Mathematical Society
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