Results 11 to 20 of about 188 (177)
CAAI Transactions on Intelligence TechnologyMonge–Ampère equations (MAEs) are fully nonlinear second‐order partial differential equations (PDEs), which are closely related to various fields including optimal transport (OT) theory, geometrical optics and affine geometry. Despite their significance,
Xinghua Pan, Zexin Feng, Kang Yang
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Action functional as an early warning indicator in the space of probability measures via Schrödinger bridge. [PDF]
Quant BiolAbstract Critical transitions and tipping phenomena between two meta‐stable states in stochastic dynamical systems are a scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway between two meta‐stable states with Onsager–Machlup action functional, to investigate the evolutionary transition dynamics ...
Zhang P, Gao T, Guo J, Duan J.
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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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Pracì Mìžnarodnogo Geometričnogo Centru, 2021 We study the relationship between structural properties of the two-dimensional nonconjugate subalgebras of the same rank of the Lie algebra of the Poincaré group P(1,4) and the properties of reduced equations for the (1+3)-dimensional homogeneous Monge ...
Vasyl Fedorchuk, Volodymyr Fedorchuk
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Backward Monge Potential and Monge-Ampere Equation
, 2021 In this paper, Monge-Kantorovich problem is considered in the infinite dimension on an abstract Wiener space $(W, H,μ)$, where $H$ is Cameron-Martin space and $μ$ is the Gaussian measure. We study the regularity of optimal transport maps with a quadratic cost function assuming that both initial and target measures have a strictly positive Radon-Nikodym
Caglar, Mine, Demirel, Ihsan
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A note on second derivative estimates for Monge-Ampère-type equations
Advanced Nonlinear Studies, 2023 In this article, we revisit previous Pogorelov-type interior and global second derivative estimates of N. S. Trudinger, F. Jiang, and J. Liu for solutions of Monge-Ampère-type partial differential equations.
Trudinger Neil S.
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A non local Monge-Ampere equation
, 2014 We introduce a non local analog to the Monge-Ampere operator and show some of its properties. We prove that a global problem involving this operator has C 1,1 solutions in the full space.
Caffarelli, Luis, Silvestre, Luis
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Convex solutions of systems arising from Monge-Ampere equations
Electronic Journal of Qualitative Theory of Differential Equations, 2009 We establish two criteria for the existence of convex solutions to a boundary value problem for weakly coupled systems arising from the Monge-Ampère equations. We shall use fixed point theorems in a cone.
Haiyan Wang
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