Zobrazeno 1 - 10
of 26
pro vyhledávání: '"Rankin, Cale"'
Autor:
Rankin, Cale, Wong, Ting-Kam Leonard
We modify the JKO scheme, which is a time discretization of Wasserstein gradient flows, by replacing the Wasserstein distance with more general transport costs on manifolds. We show when the cost function has a mixed Hessian which defines a Riemannia
Externí odkaz:
http://arxiv.org/abs/2402.17681
A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma--Trudinger--Wang condition is the Pogorelov second derivative bound. This translates to an apriori interior $C^1$ estimate for smooth optimal maps
Externí odkaz:
http://arxiv.org/abs/2311.10208
We prove the interior $C^{1,1}$ regularity of the indirect utilities which solve a subclass of principal-agent problems originally considered by Figalli, Kim, and McCann. Our approach is based on construction of a suitable comparison function which,
Externí odkaz:
http://arxiv.org/abs/2303.04937
Autor:
Rankin, Cale, Wong, Ting-Kam Leonard
Consider the Monge-Kantorovich optimal transport problem where the cost function is given by a Bregman divergence. The associated transport cost, which we call the Bregman-Wasserstein divergence, presents a natural asymmetric extension of the squared
Externí odkaz:
http://arxiv.org/abs/2302.05833
Autor:
Rankin, Cale
We provide a geometric interpretation of the well known A3w condition for regularity of optimal transport maps.
Comment: 3 pages, To appear in Bulletin of the Australian Mathematical Society
Comment: 3 pages, To appear in Bulletin of the Australian Mathematical Society
Externí odkaz:
http://arxiv.org/abs/2209.08098
Autor:
Rankin, Cale
We prove two H\"older regularity results for solutions of generated Jacobian equations. First, that under the A3 condition and the assumption of nonnegative $L^p$ valued data solutions are $C^{1,\alpha}$ for an $\alpha$ that is sharp. Then, under the
Externí odkaz:
http://arxiv.org/abs/2204.07917
Autor:
Rankin, Cale
This is a PhD thesis about generated Jacobian equations; our purpose is twofold. First, we provide an introduction to these equations, whilst, at the same time, collating some results scattered throughout the literature. The other goal is to present
Externí odkaz:
http://arxiv.org/abs/2201.02266
Autor:
Rankin, Cale
This article has two purposes. The first is to prove solutions of the second boundary value problem for generated Jacobian equations are strictly $g$-convex. The second is to prove the global $C^3$ regularity of Aleksandrov solutions to the same prob
Externí odkaz:
http://arxiv.org/abs/2111.00448
Autor:
Rankin, Cale
We present a proof of strict $g$-convexity in 2D for solutions of generated Jacobian equations with a $g$-Monge-Amp\`ere measure bounded away from 0. Subsequently this implies $C^1$ differentiability in the case of a $g$-Monge-Amp\`ere measure bounde
Externí odkaz:
http://arxiv.org/abs/2011.09042
Autor:
Rankin, Cale
Publikováno v:
Bull. Aust. Math. Soc. 102 (2020) 462-470
We prove that if two $C^{1,1}(\Omega)$ solutions of the second boundary value problem for the generated Jacobian equation intersect in $\Omega$ then they are the same solution. In addition we extend this result to $C^{2}(\overline{\Omega})$ solutions
Externí odkaz:
http://arxiv.org/abs/2002.04178