Results 51 to 60 of about 5,226,204 (223)
A curvature flow to the Lp Minkowski-type problem of q-capacity
Advanced Nonlinear Studies, 2023 This article concerns the Lp{L}_{p} Minkowski problem for q-capacity.
Liu Xinying, Sheng Weimin
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Cubo, 2022 We investigate Monge-Amp\`ere type equations on almost Hermitian manifolds and show an \textit{a priori} $L^\infty$ estimate for a smooth solution of these equations.
Masaya Kawamura
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The Monge-Ampère Equation for Freeform Optics
, 2015 The freeform shape of an optical surface is governed by the Monge-Ampère equation coupled with the transport boundary condition.
W.L. IJzerman +7 more
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Simplified Geometric Approach to Freeform Beam Shaper Design
International Journal of Optics, 2020 Beam of light shaping process can be considered ultimate, if both irradiance and wavefront spatial distributions are under control and both can be shaped arbitrarily.
Jacek Wojtanowski, Tadeusz Drozd
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Optimal global and boundary asymptotic behavior of large solutions to the Monge-Ampère equation
, 2020 This paper is mainly concerned with optimal global and boundary asymptotic behavior of strict convex large solutions to the Monge-Ampere equation det D 2 u = b ( x ) f ( u ) , x ∈ Ω , where Ω is a strict convex and bounded smooth domain in R n with n ≥ 2
Zhi-Jun Zhang
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Quantitative Linearization Results for the Monge‐Ampère Equation [PDF]
Communications on Pure and Applied Mathematics, 2019 This paper is about quantitative linearization results for the Monge‐Ampère equation with rough data. We develop a large‐scale regularity theory and prove that if a measure μ is close to the Lebesgue measure in Wasserstein distance at all scales, then ...
M. Goldman, Martin Huesmann, F. Otto
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Hyperbolic Monge-Ampère Equation
, 2006 In this paper we use the Sobolev steepest descent method introduced by John W. Neuberger to solve the hyperbolic Monge-Ampère equation. First, we use the discrete Sobolev steepest descent method to find numerical solutions; we use several initial guesses,
Howard, Tamani M.
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A Note on the Asymptotic Behavior of Parabolic Monge-Ampère Equations on Riemannian Manifolds
Journal of Applied Mathematics, 2013 We study the asymptotic behavior of the parabolic Monge-Ampère equation in , in , where is a compact complete Riemannian manifold, λ is a positive real parameter, and is a smooth function.
Qiang Ru
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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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Moser-Trudinger inequality for the complex Monge-Ampère equation [PDF]
Journal of Functional Analysis, 2020 In this paper, we prove a Moser-Trudinger type inequality for pluri-subharmonic functions vanishing on the boundary. Our proof uses a descent gradient flow for the complex Monge-Ampere functional.
Jia-Xiang Wang, Xu-Jia Wang, Bin Zhou
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