Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator

Sławomir Kołodziej

Annales Polonici Mathematici (1996)

  • Volume: 65, Issue: 1, page 11-21
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Sławomir Kołodziej. "Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator." Annales Polonici Mathematici 65.1 (1996): 11-21. <http://eudml.org/doc/270009>.

@article{SławomirKołodziej1996,
abstract = {We find a bounded solution of the non-homogeneous Monge-Ampère equation under very weak assumptions on its right hand side.},
author = {Sławomir Kołodziej},
journal = {Annales Polonici Mathematici},
keywords = {plurisubharmonic function; complex Monge-Ampère operator; capacity; Dirichlet problem},
language = {eng},
number = {1},
pages = {11-21},
title = {Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator},
url = {http://eudml.org/doc/270009},
volume = {65},
year = {1996},
}

TY - JOUR
AU - Sławomir Kołodziej
TI - Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator
JO - Annales Polonici Mathematici
PY - 1996
VL - 65
IS - 1
SP - 11
EP - 21
AB - We find a bounded solution of the non-homogeneous Monge-Ampère equation under very weak assumptions on its right hand side.
LA - eng
KW - plurisubharmonic function; complex Monge-Ampère operator; capacity; Dirichlet problem
UR - http://eudml.org/doc/270009
ER -

References

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  1. [A] H. Alexander, Projective capacity, in: Conference on Several Complex Variables, Ann. of Math. Stud. 100, Princeton Univ. Press, 1981, 3-27. 
  2. [AT] H. Alexander, and B. A. Taylor, Comparison of two capacities in n , Math. Z. 186 (1984), 407-417. Zbl0576.32029
  3. [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. 
  4. [BT1] E. Bedford and B. A. Taylor, The Dirichlet problem for a complex Monge-Ampère operator, Invent. Math. 37 (1976), 1-44. Zbl0315.31007
  5. [BT2] E. Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), 1-40. Zbl0547.32012
  6. [BL] Z. Błocki, Estimates for the complex Monge-Ampère operator, Bull. Polish Acad. Sci. Math. 41 (1993), 151-157. Zbl0795.32003
  7. [C] U. Cegrell, On the Dirichlet problem for the complex Monge-Ampère operator, Math. Z. 185 (1984), 247-251. Zbl0539.35001
  8. [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. Zbl0799.32013
  9. [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. Zbl0781.32019
  10. [D] J.-P. Demailly, Mesures de Monge-Ampère et caractérisation géométrique des variétés algébriques affines, Mém. Soc. Math. France (N.S.) 19 (1985). Zbl0579.32012
  11. [K] M. Klimek, Pluripotential Theory, Oxford University Press, 1991. 
  12. [KO] S. Kołodziej, The range of the complex Monge-Ampère operator, Indiana Univ. Math. J. 43 (1994), 1321-1338. Zbl0831.31009
  13. [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. Zbl0592.35024
  14. [P] L. Persson, On the Dirichlet problem for the complex Monge-Ampère operator, Doctoral Thesis No 1, 1992, University of Umeå. Zbl0799.32013
  15. [S] J. Siciak, Extremal Plurisubharmonic Functions and Capacities in n , Sophia University, Tokyo, 1982. Zbl0579.32025
  16. [TS] M. Tsuji, Potential Theory in Modern Function Theory, Tokyo, 1959. Zbl0087.28401

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