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On the asymptotic formula for the solution of degenerate elliptic partial differential equations

Author: Dong-Huang Wei
Journal: Proc. Amer. Math. Soc. 139 (2011), 2863-2875
MSC (2000): Primary 35J70, 32A50
Published electronically: January 7, 2011
MathSciNet review: 2801628
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Abstract: This paper gives an asymptotic expansion for the solution of the boundary problem with respect to the Laplace-Beltrami operator. We also consider some examples in the domain whose boundary is real ellipsoid, where the boundary problem does not have a $ C^n$ solution up to the boundary.

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  • 1. C. R. Graham, The Dirichlet problem for the Bergman Laplacian. I, Comm. Partial Differential Equations, 8(1983), 433-476. MR 695400 (85b:35019)
  • 2. C. R. Graham and J. Lee, Smooth solutions of degenerate Laplacians on strictly pseudoconvex domains, Duke Math. J., 57(1988), 697-720. MR 975118 (90c:32031)
  • 3. S. G. Krantz, Partial Differential Equations and Complex Analysis, CRC Press, 1992. MR 1207812 (94a:35002)
  • 4. S.-Y. Li and E. Simon, Boundary behavior of harmonic functions in metrics of Bergman type on the polydisc, Amer. J. Math., 124(2002), 1045-1057. MR 1925342 (2003h:32009)
  • 5. S.-Y. Li and D.H. Wei, On the rigidity theorem for harmonic functions in Kähler metric of Bergman type, Sci. China Math. Ser. A, 53(3)(2010), 779-790. MR 2608333
  • 6. M. Stoll, Invariant Potential Theory in the Unit Ball of $ \mathbb{C}^n$, London Math. Society Lecture Note Series, 199, Cambridge University Press, 1994. MR 1297545 (96f:31011)
  • 7. I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, Inc., Orlando, FL, 1984. MR 768584 (86g:58140)
  • 8. D. C. Chang and S.-Y. Li, A zeta function associated to the sub-Laplacian on the unit sphere in $ \mathbb{C}^n$, J. Anal. Math., 86(2002), 25-48. MR 1894476 (2003i:58062)

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Additional Information

Dong-Huang Wei
Affiliation: School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, People’s Republic of China

Received by editor(s): July 24, 2010
Received by editor(s) in revised form: July 28, 2010
Published electronically: January 7, 2011
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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