Finite element approximations of the three dimensional
          Monge-Ampère equation

Susanne Cecelia Brenner; Michael Neilan

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Displaying similar documents to “Finite element approximations of the three dimensional Monge-Ampère equation”

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. ...

On a problem of Monge.

Kantorovich, L.V. (2004)

Journal of Mathematical Sciences (New York)

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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.

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.

On decomposable Monge-Ampère equations.

Machida, Y., Morimoto, T. (1999)

Lobachevskii Journal of Mathematics

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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.

Optimality conditions and exact solutions of the two-dimensional Monge-Kantorovich problem.

Levin, V.L. (2004)

Journal of Mathematical Sciences (New York)

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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.