Weak solutions of equations of complex Monge-Ampère type
Kołodziej, Sławomir
Annales Polonici Mathematici, Tome 75 (2000), p. 59-67 / Harvested from The Polish Digital Mathematics Library
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We prove some existence results for equations of complex Monge-Ampère type in strictly pseudoconvex domains and on Kähler manifolds.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:262805 
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Kołodziej, Sławomir. Weak solutions of equations of complex Monge-Ampère type. Annales Polonici Mathematici, Tome 75 (2000) pp. 59-67. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv73z1p59bwm/

[000] [A1] T. Aubin, Equations du type Monge-Ampère sur les variétés kählériennes compactes, C. R. Acad. Sci. Paris 283 (1976), 119-121. | Zbl 0333.53040

[001] [A2] T. Aubin, Equations du type Monge-Ampère sur les variétés kählériennes compactes, Bull. Sci. Math. 102 (1978), 63-95. | Zbl 0374.53022

[002] [A3] T. Aubin, Nonlinear Analysis on Manifolds. Monge-Ampère Equations, Grundlehren Math. Wiss. 244, Springer, 1982.

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

[004] [BT2] E. Bedford and B. A. Taylor, The Dirichlet problem for an equation of complex Monge-Ampère type, in: Partial Differential Equations and Geometry, C. Byrnes (ed.), Dekker, 1979, 39-50.

[005] [BT3] E. Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), 1-40. | Zbl 0547.32012

[006] [BT4] E. Bedford and B. A. Taylor, Uniqueness for the complex Monge-Ampère equation for functions of logarithmic growth, Indiana Univ. Math. J. 38 (1989), 455-469. | Zbl 0677.32002

[007] 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), 209-252. | Zbl 0598.35048

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

[009] [K1] S. Kołodziej, The range of the complex Monge-Ampère operator II, Indiana Univ. Math. J. 44 (1995), 765-782. | Zbl 0849.31009

[010] [K2] S. Kołodziej, Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator, Ann. Polon. Math. 65 (1996), 11-21. | Zbl 0878.32014

[011] [K3] S. Kołodziej, The complex Monge-Ampère equation, Acta Math. 180 (1998), 69-117. | Zbl 0913.35043

[012] [S] Y.-T. Siu, Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics, Birkhäuser, 1987.

[013] [Y] S.-T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation, Comm. Pure Appl. Math. 31 (1978), 339-411. | Zbl 0369.53059