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On boundary blow-up problems for the complex Monge-Ampère equation


Author: Szymon Plis
Journal: Proc. Amer. Math. Soc. 136 (2008), 4355-4364
MSC (2000): Primary 32W20, 35B65
DOI: https://doi.org/10.1090/S0002-9939-08-09513-0
Published electronically: July 8, 2008
MathSciNet review: 2431050
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Abstract: We prove the $ \mathcal{C}^\infty$ regularity for some complex Monge-Ampère equations with boundary data equal to $ +\infty$.


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  • [B1] Z. Błocki, On the regularity of the complex Monge-Ampère operator, Complex geometric analysis in Pohang (1997), 181-189, Contemp. Math., 222, Amer. Math. Soc., Providence, RI, 1999. MR 1653050 (99m:32018)
  • [B2] Z. Błocki, Regularity of the degenerate Monge-Ampère equation on compact Kähler manifolds, Math. Z. 244 (2003), no. 1, 153-161. MR 1981880 (2004b:32065)
  • [C-K-N-S] L. Caffarelli, J. J. Kohn, L. Nirenberg, J. Spruck, The Dirichlet problem for non-linear second order elliptic equations, II: Complex Monge-Ampère, and uniformly elliptic equations, Comm. Pure Appl. Math. 38 (1985), 209-252. MR 780073 (87f:35097)
  • [C-Y] S.-Y. Cheng, S.-Y. Yau, On the existence of a complete Kähler metric on non-compact complex manifolds and regularity of Fefferman's equation, Comm. Pure Appl. Math. 33 (1980), 507-544. MR 575736 (82f:53074)
  • [G-P] F. Gladiali, G. Porru, Estimates for explosive solutions to p-Laplace equations, Progress in Partial Differential Equations (Pont-à-Mousson), Vol. 1, Pitman Res. Notes Math. Series, 383, Longman, Harlow (1998), 117-127. MR 1628068 (2000h:35047)
  • [I] B. Ivarsson, Regularity and uniqueness of solutions to boundary blow-up problems for the complex Monge-Ampère operator, Bull. Polish Acad. Sci. Math. 54 (2006), 13-25. MR 2270791 (2007g:32028)
  • [I-M] B. Ivarsson, J. Matero, The blow-up rate of solutions to boundary blow-up problems for the complex Monge-Ampère operator, Manuscripta Math. 120 (2006), no. 3, 325-345. MR 2243567 (2007h:32058)
  • [L-M] A. C. Lazer, P. J. McKenna, On singular boundary value problems for the Monge-Ampère operator, J. Math. Anal. Appl. 197 (1996), 341-362. MR 1372183 (97c:35064)
  • [M] A. Mohammed, On the existence of solutions to the Monge-Ampère equation with infinite boundary values, Proc. Amer. Math. Soc. 138 no. 1 (2007), 141-149. MR 2280183

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Additional Information

Szymon Plis
Affiliation: Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland
Email: splis@pk.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-08-09513-0
Keywords: Complex Monge-Amp\`ere equation, blow up problem.
Received by editor(s): November 6, 2007
Published electronically: July 8, 2008
Additional Notes: This research was partially supported by Polish grant MNiSW 3342/H03/2006/31
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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