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Remarks on elliptic problems involving the Caffarelli-Kohn-Nirenberg inequalities
Author(s):
Gongbao
Li;
Shuangjie
Peng
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1221-1228.
MSC (2000):
Primary 35J60, 35B33
Posted:
December 18, 2007
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Abstract:
We give some regularity results of the solutions and a Liouville type theorem to singular elliptic equations involving the Caffarelli-Kohn- Nirenberg inequalities.
References:
-
- 1.
- F. V. Atkinson, H. Brezis and L. A. Peletier, Nodal solutions of elliptic equations with critical Sobolev exponent, J. Differential Equations, 85(1990), 151-170. MR 1052332 (91e:35021)
- 2.
- F. V. Atkinson and L. A. Peletier, Elliptic equations with nearly critical growth, J. Differential Equations, 70(1987), 349-365. MR 915493 (89e:35054)
- 3.
- K. Chou, C. Chu, On the best constant for a weighted Sobolev-Hardy inequality, J. London Math. Soc., 48(1993), 137-151. MR 1223899 (94h:46052)
- 4.
- D. Cao, S. Peng, A note on the sign-changing solutions to elliptic problems with critical Sobolev exponent and Hardy terms, J. Differential Equations, 193(2003), 424-434. MR 1998962 (2004e:35058)
- 5.
- D. Cao, S. Peng, Asymptotic behavior for elliptic problems with singular coefficient and nearly critical Sobolev growth, Ann. Math. Pura Appl., 185(2006), 189-205. MR 2214132 (2007h:35080)
- 6.
- L. Caffarelli, R. Kohn and L. Nirenberg, First order interpolation inequality with weights, Compositio Math., 53(1984), 259-275. MR 768824 (86c:46028)
- 7.
- F. Catrina, Z. Wang, On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extermal functions, Comm. Pure Appl. Math., 54(2001), 229-258. MR 1794994 (2001k:35028)
- 8.
- L. Dupaigne, A nonlinear elliptic PDE with the inverse square potential, J. Anal. Math., 86(2002), 359-398. MR 1894489 (2003c:35046)
- 9.
- A. Ferrero, F. Gazzola, Existence of solutions for singular critical growth semilinear elliptic equations, J. Differential Equations, 177(2001), 494-522. MR 1876652 (2002m:35068)
- 10.
- V. Felli, M. Schneider, A note on regularity of solutions to degenerate critical elliptic equations of Caffarelli-Kohn-Nirenberg type, Adv. Nonlinear Stud. 3(2003) 431-443. MR 2017240 (2004k:35151)
- 11.
- B. Gidas, W-M. Ni and L. Nirenberg, Symmetry and related properties via maximum principle, Comm. Math. Phys., 68(1979), 209-243. MR 544879 (80h:35043)
- 12.
- B. Gidas and J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math., 34(1981), 525-598. MR 615628 (83f:35045)
- 13.
- E. Jannelli, The role played by space dimension in elliptic critical problems, J. Differential Equations, 156(1999), 407-426. MR 1705383 (2000f:35053)
- 14.
- D. Kang, G. Li and S. Peng, Positive solutions and critical dimensions for the elliptic problems involving the Caffarelli-Kohn-Nirenberg inequalities, preprint.
- 15.
- S. Terracini, On positive solutions to a class of equations with a singular coefficient and critical exponent, Adv. Differential Equations, 1(1996), 241-264. MR 1364003 (97b:35057)
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Additional Information:
Gongbao
Li
Affiliation:
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, People's Republic of China
Shuangjie
Peng
Affiliation:
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, People's Republic of China
DOI:
10.1090/S0002-9939-07-09229-5
PII:
S 0002-9939(07)09229-5
Received by editor(s):
August 2, 2006
Posted:
December 18, 2007
Additional Notes:
This work was partially supported by NSFC (10571069,10631030), the Key Project of the Chinese Ministry of Education (107081), and NCET-07-0350.
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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