Rafał Czyż, Lisa Hed (2008)
Annales Polonici Mathematici
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We prove that subextension of certain plurisubharmonic functions is always possible without increasing the total Monge-Ampère mass.
Kantorovich, L.V. (2004)
Journal of Mathematical Sciences (New York)
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Jonas Wiklund (2004)
Annales Polonici Mathematici
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We study two known theorems regarding Hermitian matrices: Bellman's principle and Hadamard's theorem. Then we apply them to problems for the complex Monge-Ampère operator. We use Bellman's principle and the theory for plurisubharmonic functions of finite energy to prove a version of subadditivity for the complex Monge-Ampère operator. Then we show how Hadamard's theorem can be extended to polyradial plurisubharmonic functions.
Pham Hoang Hiep (2005)
Annales Polonici Mathematici
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We give a characterization for boundedness of plurisubharmonic functions in the Cegrell class ℱ.
Machida, Y., Morimoto, T. (1999)
Lobachevskii Journal of Mathematics
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Szymon Pliś (2005)
Annales Polonici Mathematici
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We modify an example due to X.-J. Wang and obtain some counterexamples to the regularity of the degenerate complex Monge-Ampère equation on a ball in ℂⁿ and on the projective space ℙⁿ.
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.
Nguyen Quang Dieu (2011)
Annales Polonici Mathematici
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We give sufficient conditions for unicity of plurisubharmonic functions in Cegrell classes.
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.
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.
Jan Chrastina (1989)
Časopis pro pěstování matematiky
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Dieter Riebesehl, Friedmar Schulz (1984)
Mathematische Zeitschrift
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Udrişte, C., Bîlă, N. (1998)
Balkan Journal of Geometry and its Applications (BJGA)
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Yang Xing (2007)
Annales Polonici Mathematici
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We prove a decomposition theorem for complex Monge-Ampère measures of plurisubharmonic functions in connection with their pluripolar sets.
Urban Cegrell (1984)
Mathematische Zeitschrift
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John I.E. Urbas (1988)
Mathematische Zeitschrift
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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. ...