Results 1 to 10 of about 122 (113)
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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AxiomsThe Monge–Ampère operator, as a nonlinear operator embedded in parabolic differential equations, complicates the demonstration of maximal regularity for these equations.
Xingyu Liu
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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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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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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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Radial solutions for fully nonlinear elliptic equations of Monge–Ampère type
Boundary Value Problems, 2021 First, the symmetry of classical solutions to the Monge–Ampère-type equations is obtained by the moving plane method. Then, the existence and nonexistence of radial solutions in a ball are got from the symmetry results.
Limei Dai, Huihui Cheng, Hongfei Li
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On some exact solutions of heavenly equations in four dimensions
AIP Advances, 2020 Some new classes of exact solutions (so-called functionally invariant solutions) of the elliptic and hyperbolic complex Monge–Ampère equations and of the second heavenly equation are found. Besides, non-invariance of the found classes of solutions of the
Ł. T. Stȩpień
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Bäcklund Transformations for Liouville Equations with Exponential Nonlinearity
Axioms, 2021 This work aims to obtain new transformations and auto-Bäcklund transformations for generalized Liouville equations with exponential nonlinearity having a factor depending on the first derivatives.
Tatyana V. Redkina +3 more
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