Results 11 to 20 of about 1,758 (174)
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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IET Microwaves, Antennas & Propagation, 2023 This study proposes an analytical formulation in complex coordinates to synthesise three‐dimensional single‐shell dielectric lens surfaces. An exact formulation based on geometrical optics is developed, and the synthesis problem is modelled as a non ...
Aline Rocha deAssis +2 more
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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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Monotone discretization of the Monge-Ampère equation of optimal transport
, 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.
Guillaume Bonnet +3 more
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Regularity of solutions to the quaternionic Monge-Ampère equation [PDF]
, 2020 The regularity of solutions to the Dirichlet problem for the quaternionic Monge-Ampère equation is discussed. We prove that the solution to the Dirichlet problem is Hölder continuous under some conditions on the boundary values and the quaternionic Monge-
Kołodziej, Sławomir, Sroka, Marcin
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Geodesics in the space of relatively Kähler metrics
Journal of the London Mathematical Society, Volume 108, Issue 3, Page 1036-1081, September 2023., 2023 Abstract We derive the geodesic equation for relatively Kähler metrics on fibrations and prove that any two such metrics with fibrewise constant scalar curvature are joined by a unique smooth geodesic. We then show convexity of the log‐norm functional for this setting along geodesics, which yields simple proofs of Dervan and Sektnan's uniqueness result
Michael Hallam
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Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems
Communications on Pure and Applied Mathematics, Volume 76, Issue 8, Page 1554-1607, August 2023., 2023 Abstract For a given finite subset S of a compact Riemannian manifold (M,g) whose Schouten curvature tensor belongs to a given cone, we establish a necessary and sufficient condition for the existence and uniqueness of a conformal metric on M\S such that each point of S corresponds to an asymptotically flat end and that the Schouten tensor of the ...
Yanyan Li, Luc Nguyen
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Massively parallel computation of globally optimal shortest paths with curvature penalization
Concurrency and Computation: Practice and Experience, Volume 35, Issue 2, 25 January 2023., 2023 Abstract We address the computation of paths globally minimizing an energy involving their curvature, with given endpoints and tangents at these endpoints, according to models known as the Reeds‐Shepp car (reversible and forward variants), the Euler‐Mumford elasticae, and the Dubins car. For that purpose, we numerically solve degenerate variants of the
Jean‐Marie Mirebeau +4 more
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