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.
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Displaying similar documents to “Continuous and estimates for the complex Monge-Ampère equation on bounded domains in .”
Weak solutions to the complex Monge-Ampère equation on hyperconvex domains
Weak solutions of equations of complex Monge-Ampère type
Sławomir Kołodziej (2000)
Annales Polonici Mathematici
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We prove some existence results for equations of complex Monge-Ampère type in strictly pseudoconvex domains and on Kähler manifolds.
On a problem of Monge.
Kantorovich, L.V. (2004)
Journal of Mathematical Sciences (New York)
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On decomposable Monge-Ampère equations.
Machida, Y., Morimoto, T. (1999)
Lobachevskii Journal of Mathematics
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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 the Dirichlet Problem for the Complex Monge-Ampère Operator.
Urban Cegrell (1984)
Mathematische Zeitschrift
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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.
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.
A Priori Estimates and a Liouvielle Theorem for Complex Monge-Ampère Equations.
Dieter Riebesehl, Friedmar Schulz (1984)
Mathematische Zeitschrift
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Nontrivial solutions for Monge-Ampère type operators in convex domains.
B. Franchi, N. Kutev, S. Polidoro (1993)
Manuscripta mathematica
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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.
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.
Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator
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.
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.
The complex Monge-Ampère operator in the Cegrell classes
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.
Counterexample to Regularity for the Complex Monge-Ampère Equation.
John Erik Fornaess, Eric Bedford (1978/79)
Inventiones mathematicae
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A general Dirichlet problem for the complex Monge-Ampère operator
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.
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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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.