Existence of C... local Solutions for the Monge-Ampère equation.
J., Zuily, C. Hong (1987)
Inventiones mathematicae
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Displaying similar documents to “Global Hölder estimates for equations of Monge-Ampère type.”
Existence of C... local Solutions for the Monge-Ampère equation.
The Dirchlet Problem for a Complex Monge-Ampère Equation.
Eric Bedford, B.A. Taylor (1976)
Inventiones mathematicae
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Counterexample to Regularity for the Complex Monge-Ampère Equation.
John Erik Fornaess, Eric Bedford (1978/79)
Inventiones mathematicae
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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 Priori Estimates and a Liouvielle Theorem for Complex Monge-Ampère Equations.
Dieter Riebesehl, Friedmar Schulz (1984)
Mathematische Zeitschrift
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Regularity of Generalized Solutions of Monge-Ampère Equations.
John I.E. Urbas (1988)
Mathematische Zeitschrift
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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.
On decomposable Monge-Ampère equations.
Machida, Y., Morimoto, T. (1999)
Lobachevskii Journal of Mathematics
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The Bieberbach-Rademacher problem for the Monge-Ampère operator.
Jerk Matero (1996)
Manuscripta mathematica
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An energy estimate for the complex Monge-Ampère operator
Urban Cegrell, Leif Persson (1997)
Annales Polonici Mathematici
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We prove an energy estimate for the complex Monge-Ampère operator, and a comparison theorem for the corresponding capacity and energy. The results are pluricomplex counterparts to results in classical potential theory.
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.
Regularity and Uniqueness of Solutions to Boundary Blow-up Problems for the Complex Monge-Ampère Operator
Björn Ivarsson (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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We prove that plurisubharmonic solutions to certain boundary blow-up problems for the complex Monge-Ampère operator are Lipschitz continuous. We also prove that in certain cases these solutions are unique.
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.
The Dirichlet problem for the degenerate Monge-Ampère equation.
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.