Results 1 to 10 of about 169 (160)
A Monge–Ampere Equation with an Unusual Boundary Condition [PDF]
Symmetry, 2015 We consider a class of Monge–Ampere equations where the convex conjugate of the unknown function is prescribed on a boundary of its domain yet to be determined. We show the existence of a weak solution.
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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 sharp global estimate and an overdetermined problem for Monge-Ampère type equations
Advanced Nonlinear Studies, 2022 We consider Monge-Ampère type equations involving the gradient that are elliptic in the framework of convex functions. Through suitable symmetrization we find sharp estimates to solutions of such equations.
Mohammed Ahmed, Porru Giovanni
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Numerically solving generated Jacobian equations in freeform optical design [PDF]
EPJ Web of Conferences, 2020 We present an efficient numerical algorithm that can be used to solve the generalized Monge-Ampère equations for a single freeform reflector and lens surface.
Romijn Lotte B. +3 more
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Hybridizable Discontinuous Galerkin Methods for the Monge–Ampere Equation
, 2023 We introduce two hybridizable discontinuous Galerkin (HDG) methods for numerically solving the Monge-Ampere equation. The first HDG method is devised to solve the nonlinear elliptic Monge-Ampere equation by using Newton's method. The second HDG method is devised to solve a sequence of the Poisson equation until convergence to a fixed-point solution of ...
Ngoc Cuong Nguyen, Jaime Peraire
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Advances in Nonlinear Analysis, 2020 In this paper, the equations and systems of Monge-Ampère with parameters are considered. We first show the uniqueness of of nontrivial radial convex solution of Monge-Ampère equations by using sharp estimates.
Feng Meiqiang
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Advanced Nonlinear Studies, 2023 We consider the asymptotic behavior of solutions to the Monge-Ampère equations with slow convergence rate at infinity and fulfill previous results under faster convergence rate by Bao et al. [Monge-Ampère equation on exterior domains, Calc. Var PDE.
Liu Zixiao, Bao Jiguang
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The Dirichlet problem for degenerate complex Monge–Ampere equations [PDF]
Communications in Analysis and Geometry, 2010 The Dirichlet problem for a Monge-Ampere equation corresponding to a nonnegative, possible degenerate cohomology class on a Kaehler manifold with boundary is studied. C^{1,α} estimates away from a divisor are obtained, by combining techniques of Blocki, Tsuji, Yau, and pluripotential theory.
Phong, D. H., Sturm, Jacob
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The exterior Dirichlet problems of Monge–Ampère equations in dimension two
Boundary Value Problems, 2020 In this paper, we study the Monge–Ampère equations det D 2 u = f $\det D^{2}u=f$ in dimension two with f being a perturbation of f 0 $f_{0}$ at infinity.
Limei Dai
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Comptes Rendus. Mathématique, 2023 In this paper, we consider the asymptotic behavior of solutions of Monge–Ampère equations with general boundary value conditions in half spaces, which reveals the accurate effect of boundary value condition on asymptotic behavior and improves the result ...
Jia, Xiaobiao, Li, Xuemei
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