On a problem of Monge.
Kantorovich, L.V. (2004)
Journal of Mathematical Sciences (New York)
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Displaying similar documents to “Radially symmetric plurisubharmonic functions”
On a problem of Monge.
Subextension of plurisubharmonic functions without increasing the total Monge-Ampère mass
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.
Symmetry Lie group of the Monge-Ampère equation.
Udrişte, C., Bîlă, N. (1998)
Balkan Journal of Geometry and its Applications (BJGA)
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Regularity of The Complex Monge-Ampere Equation for Radially Symmetric Functions of the Unit Ball.
David Monn (1986)
Mathematische Annalen
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A decomposition of complex Monge-Ampère measures
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.
On decomposable Monge-Ampère equations.
Machida, Y., Morimoto, T. (1999)
Lobachevskii Journal of Mathematics
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A characterization of bounded 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.
Matrix inequalities and the complex Monge-Ampère operator
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.
Weak solutions to the complex Monge-Ampère equation on hyperconvex domains
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.
Symmetry Lie group of the Monge-Ampère equation.
Udrişte, C., Bîlă, N. (1999)
APPS. Applied Sciences
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A counterexample to the regularity of the degenerate complex Monge-Ampère equation
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.
A unicity theorem for plurisubharmonic functions
Nguyen Quang Dieu (2011)
Annales Polonici Mathematici
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We give sufficient conditions for unicity of plurisubharmonic functions in Cegrell classes.
Finite element approximations of the three dimensional Monge-Ampère equation
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. ...