Results 91 to 100 of about 1,758 (174)

Contact Geometry of Hyperbolic Equations of Generic Type

Symmetry, Integrability and Geometry: Methods and Applications, 2008
We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampère (class 6-6), Goursat (class 6-7) and generic (class 7-7 ...
Dennis The
doaj   +1 more source

Global interval bifurcation and convex solutions for the Monge-Ampere equations

Electronic Journal of Differential Equations, 2018
In this article, we establish the global bifurcation result from the trivial solutions axis or from infinity for the Monge-Ampere equations with non-differentiable nonlinearity. By applying the above result, we shall determine the interval of $\gamma$
Wenguo Shen
doaj  

Design of freeform mirrors using the concentric rings method. [PDF]

Heliyon, 2023
González-García J, Santiago-Alvarado A, Cruz-Félix AS.   +2 more
europepmc   +1 more source

Two-scale method for the Monge–Ampère equation: pointwise error estimates

, 2018
In this paper we continue the analysis of the two-scale method for the Monge–Ampère equation for dimension d ≥ 2 introduced in the study by Nochetto et al. (2017, Two-scale method for the Monge–Ampère equation: convergence to the viscosity solution. Math.
D Ntogkas, R H Nochetto, W Zhang
core   +1 more source

Optimal transport and control of active drops. [PDF]

Proc Natl Acad Sci U S A, 2022
Shankar S, Raju V, Mahadevan L.
europepmc   +1 more source

Illumination freeform design using Monge-Ampère equations

, 2019
\u3cp\u3eAs a generic model for freeform optical systems, we combine the optical map and the luminous flux conservation law into a generalized Monge-Ampère equation.
IJzerman, WL Wilbert, ten Thije Boonkkamp, Jan H.M., W.L. IJzerman, Thije Boonkkamp, JHM Jan ten, J.H.M. ten Thije Boonkkamp, IJzerman, Wilbert L.   +5 more
core   +1 more source

Hybridizable Discontinuous Galerkin Methods for the Two-Dimensional Monge–Ampère Equation

We introduce two hybridizable discontinuous Galerkin (HDG) methods for numerically solving the two-dimensional Monge–Ampère equation. The first HDG method is devised to solve the nonlinear elliptic Monge–Ampère equation by using Newton’s method.
Nguyen, Ngoc C., Peraire, Jaime
core   +1 more source

Interior C² estimate for monge-ampère equation in dimension two

, 2021
We obtain a genuine local C estimate for the Monge-Ampère equation in dimension two, by using the partial Legendre transform.
Jiakun Liu (14168568)
core  

Monge-Ampère gravity, optimal transport theory and their link to the Galileons

International audienceMathematicians have been proposing for sometimes that Monge-Ampère equation, a nonlinear generalization of the Poisson equation, where trace of the Hessian is replaced by its determinant, provides an alternative non-relativistic ...
Brenier, Yann, Mohayaee, Roya, Bonnefous, Albert   +2 more
core   +2 more sources

Regularity of center-outward distribution functions in non-convex domains

Advanced Nonlinear Studies
For a probability P in Rd ${\mathbb{R}}^{d}$ its center outward distribution function F ±, introduced in V. Chernozhukov, A. Galichon, M. Hallin, and M. Henry (“Monge–Kantorovich depth, quantiles, ranks and signs,” Ann. Stat., vol. 45, no. 1, pp.
del Barrio Eustasio, González-Sanz Alberto   +1 more
doaj   +1 more source