On the Dirichlet Problem for the Complex Monge-Ampère Operator.
Urban Cegrell (1984)
Mathematische Zeitschrift
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Urban Cegrell (1984)
Mathematische Zeitschrift
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Jiaxing Hong (1992)
Mathematische Zeitschrift
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Urban Cegrell (2008)
Annales Polonici Mathematici
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We study a general Dirichlet problem for the complex Monge-Ampère operator, with maximal plurisubharmonic functions as boundary data.
Sławomir Kołodziej (1996)
Annales Polonici Mathematici
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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.
John I.E. Urbas (1988)
Mathematische Zeitschrift
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Luis A. Caffarelli, Louis Nirenberg, Joel Spruck (1986)
Revista Matemática Iberoamericana
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Let Ω be a bounded convex domain in Rn with smooth, strictly convex boundary ∂Ω, i.e. the principal curvatures of ∂Ω are all positive. We study the problem of finding a convex function u in Ω such that: det (uij) = 0 in Ω u = φ given on ∂Ω.
U. Cegrell, Azim Sadullaev (1992)
Mathematica Scandinavica
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Slimane Benelkourchi (2014)
Annales Polonici Mathematici
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We show a very general existence theorem for a complex Monge-Ampère type equation on hyperconvex domains.
Mitsuru Nakai, Leo Sario (1971)
Mathematische Zeitschrift
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S. Minakshisundaram (1962)
Mathematische Zeitschrift
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David Monn (1986)
Mathematische Annalen
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Dieter Riebesehl, Friedmar Schulz (1984)
Mathematische Zeitschrift
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Rafał Czyż
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The complex Monge-Ampère operator is a useful tool not only within pluripotential theory, but also in algebraic geometry, dynamical systems and Kähler geometry. In this self-contained survey we present a unified theory of Cegrell's framework for the complex Monge-Ampère operator.
Bhaskar Bagchi (1982)
Mathematische Zeitschrift
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Urban Cegrell (1986)
Mathematische Zeitschrift
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