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 “An eigenvalue problem for the complex Monge-Ampère operator in pseudoconvex domains”
Weak solutions to the complex Monge-Ampère equation on hyperconvex domains
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.
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.
Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator
P. Delanoë (1991)
Annales de l'I.H.P. Analyse non linéaire
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On a problem of Monge.
Kantorovich, L.V. (2004)
Journal of Mathematical Sciences (New York)
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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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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.
The complex Monge-Ampère operator in hyperconvex domains
Zbigniew Błocki (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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.
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.
On the Dirichlet Problem for the Complex Monge-Ampère Operator.
Urban Cegrell (1984)
Mathematische Zeitschrift
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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.
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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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.
Counterexample to Regularity for the Complex Monge-Ampère Equation.
John Erik Fornaess, Eric Bedford (1978/79)
Inventiones mathematicae
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