Zobrazeno 1 - 10
of 2 472
pro vyhledávání: '"Monge Ampère Equation"'
Publikováno v:
Advanced Nonlinear Studies, Vol 24, Iss 4, Pp 880-894 (2024)
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,
Externí odkaz:
https://doaj.org/article/c1c19dd0dc5d40bcb8b20845192ed9df
Autor:
Zhilin Yang
Publikováno v:
Mathematical Biosciences and Engineering, Vol 20, Iss 12, Pp 20959-20970 (2023)
This paper deals with the existence and multiplicity of convex radial solutions for the Monge-Amp$ \grave{\text e} $re equation involving the gradient $ \nabla u $: $ \begin{cases} \det (D^2u) = f(|x|, -u, |\nabla u|), x\in B, \\ u|_{\partial B} =
Externí odkaz:
https://doaj.org/article/15fd36fbc86640d58faca88571c327a5
Autor:
Connor Mooney, Arghya Rakshit
Publikováno v:
Mathematics in Engineering, Vol 5, Iss 5, Pp 1-11 (2023)
We construct new examples of Monge-Ampère metrics with polyhedral singular structures, motivated by problems related to the optimal transport of point masses and to mirror symmetry. We also analyze the stability of the singular structures under smal
Externí odkaz:
https://doaj.org/article/ef685e83b7ad40fabc5f82553278ad56
Publikováno v:
Comptes Rendus. Mécanique, Vol , Iss , Pp 1-16 (2023)
We address the numerical solution of the Dirichlet problem for the two-dimensional elliptic Monge–Ampère equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators from the nonl
Externí odkaz:
https://doaj.org/article/7ce8052ed6ed45c3a6cd24f964a943d5
Publikováno v:
Advanced Nonlinear Studies, Vol 23, Iss 1, Pp 375-417 (2023)
In this note, we establish the global C3,α{C}^{3,\alpha } regularity for potential functions in optimal transportation between hypercubes in Rn{{\mathbb{R}}}^{n} for n≥3n\ge 3. When n=2n=2, the result was proved by Jhaveri. The C3,α{C}^{3,\alpha
Externí odkaz:
https://doaj.org/article/f51ed278e7834ae1b5350933cd2acf35
Autor:
Chen Zhengmao
Publikováno v:
Advanced Nonlinear Studies, Vol 23, Iss 1, Pp 783-827 (2023)
In the present article, we prove the existence and uniqueness of smooth solutions to an anisotropic Lp{L}_{p} Minkowski problem for the log-concave measure. Our proof of the existence is based on the well-known continuous method whose crucial factor
Externí odkaz:
https://doaj.org/article/5fd3d2143cb64331a4feb5c829c2f387
Autor:
Yu Yuan
Publikováno v:
Mathematics in Engineering, Vol 5, Iss 2, Pp 1-6 (2023)
We present an integral approach to Pogorelov's Hessian estimates for the Monge-Ampère equation, originally obtained via a pointwise argument.
Externí odkaz:
https://doaj.org/article/f5c52257753d4648aa992fd759426bcb
Autor:
Figalli Alessio, Jhaveri Yash
Publikováno v:
Advanced Nonlinear Studies, Vol 23, Iss 1, Pp 365-417 (2023)
In this note, we extend the regularity theory for monotone measure-preserving maps, also known as optimal transports for the quadratic cost optimal transport problem, to the case when the support of the target measure is an arbitrary convex domain an
Externí odkaz:
https://doaj.org/article/55c2c27b63174d36af04c0bb9052d637
Autor:
Jian Huaiyu, Wang Xianduo
Publikováno v:
Advances in Nonlinear Analysis, Vol 12, Iss 1, Pp 39-63 (2023)
In this article, we study the asymptotic behaviour at infinity for viscosity solutions to a singular Monge-Ampère equation in half space from affine geometry. In particular, we extend the Liouville theorem for smooth solutions to the case of viscosi
Externí odkaz:
https://doaj.org/article/38e8ef908d074316ab90a489e1840c35
Autor:
Zhengmao Chen
Publikováno v:
AIMS Mathematics, Vol 8, Iss 6, Pp 13134-13153 (2023)
In the present paper, we prove the a priori bounds and existence of smooth solutions to a Minkowski type problem for the log-concave measure $ e^{-f(|x|^2)}dx $ in warped product space forms with zero sectional curvature. Our proof is based on the me
Externí odkaz:
https://doaj.org/article/782c791f1b5a490aab2a267f60ebd155