Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator
Sławomir Kołodziej
Annales Polonici Mathematici, Tome 63 (1996), p. 11-21 / Harvested from The Polish Digital Mathematics Library
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We find a bounded solution of the non-homogeneous Monge-Ampère equation under very weak assumptions on its right hand side.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:270009 
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Sławomir Kołodziej. Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator. Annales Polonici Mathematici, Tome 63 (1996) pp. 11-21. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv65z1p11bwm/

[000] [A] H. Alexander, Projective capacity, in: Conference on Several Complex Variables, Ann. of Math. Stud. 100, Princeton Univ. Press, 1981, 3-27.

[001] [AT] H. Alexander, and B. A. Taylor, Comparison of two capacities in ℂn, Math. Z. 186 (1984), 407-417. | Zbl 0576.32029

[002] [B] E. Bedford, Survey of pluri-potential theory, in: Several Complex Variables: Proceedings of the Mittag-Leffler Inst. 1987-1988, J. E. Fornaess (ed.), Math. Notes 38, Princeton University Press, 1993, 48-97.

[003] [BT1] E. Bedford and B. A. Taylor, The Dirichlet problem for a complex Monge-Ampère operator, Invent. Math. 37 (1976), 1-44. | Zbl 0315.31007

[004] [BT2] E. Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), 1-40. | Zbl 0547.32012

[005] [BL] Z. Błocki, Estimates for the complex Monge-Ampère operator, Bull. Polish Acad. Sci. Math. 41 (1993), 151-157. | Zbl 0795.32003

[006] [C] U. Cegrell, On the Dirichlet problem for the complex Monge-Ampère operator, Math. Z. 185 (1984), 247-251. | Zbl 0539.35001

[007] [CP] U. Cegrell, and L. Persson, The Dirichlet problem for the complex Monge-Ampère operator: stability in L², Michigan Math. J. 39 (1992), 145-151. | Zbl 0799.32013

[008] [CS] U. Cegrell and A. Sadullaev, Approximation of plurisubharmonic functions and the Dirichlet problem for the complex Monge-Ampère operator, Math. Scand. 71 (1993), 62-68. | Zbl 0781.32019

[009] [D] J.-P. Demailly, Mesures de Monge-Ampère et caractérisation géométrique des variétés algébriques affines, Mém. Soc. Math. France (N.S.) 19 (1985). | Zbl 0579.32012

[010] [K] M. Klimek, Pluripotential Theory, Oxford University Press, 1991.

[011] [KO] S. Kołodziej, The range of the complex Monge-Ampère operator, Indiana Univ. Math. J. 43 (1994), 1321-1338. | Zbl 0831.31009

[012] [M] D. R. Monn, Regularity of the complex Monge-Ampère equation for radially symmetric functions of the unit ball, Math. Ann. 275 (1986), 501-511. | Zbl 0592.35024

[013] [P] L. Persson, On the Dirichlet problem for the complex Monge-Ampère operator, Doctoral Thesis No 1, 1992, University of Umeå. | Zbl 0799.32013

[014] [S] J. Siciak, Extremal Plurisubharmonic Functions and Capacities in ℂn, Sophia University, Tokyo, 1982. | Zbl 0579.32025

[015] [TS] M. Tsuji, Potential Theory in Modern Function Theory, Tokyo, 1959. | Zbl 0087.28401