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A new maximum principle of elliptic differential equations in divergence form
Author(s):
Dongsheng
Li;
Lihe
Wang
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2823-2828.
MSC (2000):
Primary 35J25
Posted:
April 15, 2008
MathSciNet review:
2399046
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Abstract:
In this paper will be presented a new maximum principle of elliptic differential equations in divergence form which can be regarded as the counterpart of the Alexandroff-Bakelman-Pucci maximum principle of elliptic differential equations in nondivergence form.
References:
-
- 1.
- Caffarelli, L. A., and Cabre, X., Fully nonlinear elliptic equations, Colloquium Publications, 43, Amer. Math. Soc., Providence, RI, 1995. MR 1351007 (96h:35046)
- 2.
- Gilbarg, D., and Trudinger, N. S., Elliptic partial differential equations of second order, 2nd ed., Springer-Verlag, 1983. MR 737190 (86c:35035)
- 3.
- Lewy, H., and Stampacchia, G., On the regularity of the solution of a variational inequality, Comm. on Pure and Appl. Math., 1969, XXII, 153-188. MR 0247551 (40:816)
- 4.
- Lions, J.-L., and Stampacchia, G., Variational inequalities, Comm. on Pure and Appl. Math., 1967, XX, 493-519. MR 0216344 (35:7178)
- 5.
- Talenti, G., Elliptic equations and rearrangements, Annali della Scuola Norm. Sup. di Pisa, 1976, 3, 697-718. MR 0601601 (58:29170)
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Additional Information:
Dongsheng
Li
Affiliation:
College of Science, Xi'an Jiaotong University, Xi'an 710049, China
Email:
lidsh@mail.xjtu.edu.cn
Lihe
Wang
Affiliation:
Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242-1419
Email:
lwang@math.uiowa.edu
DOI:
10.1090/S0002-9939-08-09561-0
PII:
S 0002-9939(08)09561-0
Keywords:
Maximum principle,
elliptic equation in divergence form.
Received by editor(s):
August 1, 2005,
Received by editor(s) in revised form:
January 20, 2007
Posted:
April 15, 2008
Additional Notes:
The first author was supported by the NSF of China: 10771166
The second author was supported by PCSIRT
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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