Local regularity for concave homogeneous complex degenerate elliptic equations dominating the Monge–Ampère equation [PDF]
Annali di Matematica Pura ed Applicata, 2021 In this paper, we establish a local regularity result for Wloc2,p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\
Soufian Abja, Guillaume Olive
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The Initial and Neumann Boundary Value Problem for a Class Parabolic Monge-Ampère Equation [PDF]
Abstract and Applied Analysis, 2013 We consider the existence, uniqueness, and asymptotic behavior of a classical solution to the initial and Neumann boundary value problem for a class nonlinear parabolic equation of Monge-Ampère type. We show that such solution exists for all times and is
Juan Wang, Jinlin Yang, Xinzhi Liu
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The complex Monge-Ampère equation on compact Hermitian manifolds [PDF]
, 2009 We show that, up to scaling, the complex Monge-Ampere equation on compact Hermitian manifolds always admits a smooth solution.
Valentino Tosatti, B. Weinkove
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Monotone discretization of the Monge-Ampère equation of optimal transport
ESAIM: Mathematical Modelling and Numerical Analysis, 2022 We design a monotone finite difference discretization of the second boundary value problem for the Monge-Ampère equation, whose main application is optimal transport.
G. Bonnet, J. Mirebeau
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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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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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Pseudo-Riemannian and Hessian geometry related to Monge-Ampère structures [PDF]
, 2022 summary:We study properties of pseudo-Riemannian metrics corresponding to Monge-Ampère structures on four dimensional $T^*M$. We describe a family of Ricci flat solutions, which are parametrized by six coefficients satisfying the Plücker embedding ...
Suchánek, R., Hronek, S.
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Design of optical surfaces conform the hyperbolic Monge-Ampère equation [PDF]
EPJ Web of Conferences, 2022 We present a method for designing freeform optical surfaces for illumination optics. By the laws of reflection, refraction and conservation of energy, a fully nonlinear PDE, the Monge-Ampere equation, is derived for the optical surface.
Bertens M.W.M.C. +3 more
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A monotonicity approach to Pogorelov's Hessian estimates for Monge- Ampère equation
Mathematics in Engineering, 2022 We present an integral approach to Pogorelov's Hessian estimates for the Monge-Ampère equation, originally obtained via a pointwise argument.
Yu Yuan
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