Continuous and Lp estimates for the complex Monge-Ampère equation on bounded domains in ℂn
International Journal of Mathematics and Mathematical Sciences, 2002 Continuous solutions with continuous data and Lp solutions with Lp data are obtained for the complex Monge-Ampère equation on bounded domains, without requiring any smoothness of the domains.
Patrick W. Darko
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Application of isotropic geometry to the solution of the Monge–Ampere equation
Қарағанды университетінің хабаршысы. Математика сериясыThis paper explores the Monge–Ampere equation in the context of isotropic geometry. The study begins with an overview of the fundamental properties of isotropic space, including its scalar product, distance formula, and the nature of surfaces and ...
Sh.Sh. Ismoilov
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A curvature flow to the Lp Minkowski-type problem of q-capacity
Advanced Nonlinear Studies, 2023 This article concerns the Lp{L}_{p} Minkowski problem for q-capacity.
Liu Xinying, Sheng Weimin
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EURECOM:Monthly Bulletin of European Community Economic and Financial News. January 1999 Vol. 11, No. 1 [PDF]
, 1999 We show here a weak Hölder regularity up to the boundary of the solution to the Dirichlet problem for the complex Monge-Ampère equation with data in the Lp space and Ω satisfying an f-property.
Baracco, Luca +2 more
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Simplified Geometric Approach to Freeform Beam Shaper Design
International Journal of Optics, 2020 Beam of light shaping process can be considered ultimate, if both irradiance and wavefront spatial distributions are under control and both can be shaped arbitrarily.
Jacek Wojtanowski, Tadeusz Drozd
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Cubo, 2022 We investigate Monge-Amp\`ere type equations on almost Hermitian manifolds and show an \textit{a priori} $L^\infty$ estimate for a smooth solution of these equations.
Masaya Kawamura
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On sharp lower bounds for Calabi type functionals and destabilizing properties of gradient flows
, 2020 Let $X$ be a compact K\"ahler manifold with a given ample line bundle $L$. In \cite{Don05}, Donaldson proved that the Calabi energy of a K\"ahler metric in $c_1(L)$ is bounded from below by the supremum of a normalized version of the minus Donaldson ...
Xia, Mingchen
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Convergence of the weak K\"ahler-Ricci Flow on manifolds of general type
, 2019 We study the K\"ahler-Ricci flow on compact K\"ahler manifolds whose canonical bundle is big. We show that the normalized K\"ahler-Ricci flow has long time existence in the viscosity sense, is continuous in a Zariski open set, and converges to the unique
Tô, Tat Dat
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Discretization of the 3D Monge-Ampere operator, between Wide Stencils and Power Diagrams [PDF]
, 2015 We introduce a monotone (degenerate elliptic) discretization of the Monge-Ampere operator, on domains discretized on cartesian grids. The scheme is consistent provided the solution hessian condition number is uniformly bounded.
Mirebeau, Jean-Marie
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A Note on the Asymptotic Behavior of Parabolic Monge-Ampère Equations on Riemannian Manifolds
Journal of Applied Mathematics, 2013 We study the asymptotic behavior of the parabolic Monge-Ampère equation in , in , where is a compact complete Riemannian manifold, λ is a positive real parameter, and is a smooth function.
Qiang Ru
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