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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.
Urban Cegrell (1984)
Mathematische Zeitschrift
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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.
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.
Bert G. Wachsmuth (1992)
Mathematische Zeitschrift
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B. Franchi, N. Kutev, S. Polidoro (1993)
Manuscripta mathematica
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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.
Susanne Cecelia Brenner, Michael Neilan (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
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In this paper, we construct and analyze finite element methods for the three dimensional Monge-Ampère equation. We derive methods using the Lagrange finite element space such that the resulting discrete linearizations are symmetric and stable. With this in hand, we then prove the well-posedness of the method, as well as derive quasi-optimal error estimates. We also present some numerical experiments that back up the theoretical findings. ...