On boundary blow-up problems for the complex Monge-Ampère equation
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Abstract:
We prove the $\mathcal {C}^\infty$ regularity for some complex Monge-Ampère equations with boundary data equal to $+\infty$.References
- Zbigniew Błocki, On the regularity of the complex Monge-Ampère operator, Complex geometric analysis in Pohang (1997), Contemp. Math., vol. 222, Amer. Math. Soc., Providence, RI, 1999, pp. 181–189. MR 1653050, DOI 10.1090/conm/222/03161
- Zbigniew Błocki, Regularity of the degenerate Monge-Ampère equation on compact Kähler manifolds, Math. Z. 244 (2003), no. 1, 153–161. MR 1981880, DOI 10.1007/s00209-002-0483-x
- L. Caffarelli, J. J. Kohn, L. Nirenberg, and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations. II. Complex Monge-Ampère, and uniformly elliptic, equations, Comm. Pure Appl. Math. 38 (1985), no. 2, 209–252. MR 780073, DOI 10.1002/cpa.3160380206
- Shiu Yuen Cheng and Shing Tung Yau, On the existence of a complete Kähler metric on noncompact complex manifolds and the regularity of Fefferman’s equation, Comm. Pure Appl. Math. 33 (1980), no. 4, 507–544. MR 575736, DOI 10.1002/cpa.3160330404
- Francesca Gladiali and Giovanni Porru, Estimates for explosive solutions to $p$-Laplace equations, Progress in partial differential equations, Vol. 1 (Pont-à-Mousson, 1997) Pitman Res. Notes Math. Ser., vol. 383, Longman, Harlow, 1998, pp. 117–127. MR 1628068
- Björn Ivarsson, Regularity and uniqueness of solutions to boundary blow-up problems for the complex Monge-Ampère operator, Bull. Pol. Acad. Sci. Math. 54 (2006), no. 1, 13–25. MR 2270791, DOI 10.4064/ba54-1-2
- Björn Ivarsson and Jerk 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, DOI 10.1007/s00229-006-0017-7
- A. C. Lazer and P. J. McKenna, On singular boundary value problems for the Monge-Ampère operator, J. Math. Anal. Appl. 197 (1996), no. 2, 341–362. MR 1372183, DOI 10.1006/jmaa.1996.0024
- Ahmed Mohammed, On the existence of solutions to the Monge-Ampère equation with infinite boundary values, Proc. Amer. Math. Soc. 135 (2007), no. 1, 141–149. MR 2280183, DOI 10.1090/S0002-9939-06-08623-0
Additional Information
- Szymon Pliś
- Affiliation: Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland
- Email: splis@pk.edu.pl
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2431050