On Hölder continuity in time of the optimal transport map towards measures along a curve
نویسنده
چکیده
We discuss the problem of the regularity in time of the map t 7→ Tt ∈ L(R,R;σ) where Tt is a transport map (optimal or not) from a reference measure σ to a measure μt which lies along an absolutely continuous curve t 7→ μt in the space (Pp(R),Wp). We prove that in most cases such a map is no more than 1 p -Hölder continuous.
منابع مشابه
Continuity of optimal transport maps and convexity of injectivity domains on small deformations of S
Given a compact Riemannian manifold, we study the regularity of the optimal transport map between two probability measures with cost given by the squared Riemannian distance. Our strategy is to define a new form of the so-called Ma-Trudinger-Wang condition and to show that this condition, together with the strict convexity on the nonfocal domains, implies the continuity of the optimal transport...
متن کاملMass Transportation on Sub-Riemannian Manifolds
We study the optimal transport problem in sub-Riemannian manifolds where the cost function is given by the square of the sub-Riemannian distance. Under appropriate assumptions, we generalize Brenier-McCann’s Theorem proving existence and uniqueness of the optimal transport map. We show the absolute continuity property of Wassertein geodesics, and we address the regularity issue of the optimal m...
متن کاملReducing CO2 Emissions from Road Transport - Overview of the Main Initiatives and Technical Measures Proposed to Date in Europe
The demand for fossil fuel in the transport sector is constantly increasing and transportation is ranked amongst the highest greenhouse emitting sectors globally. Today, tackling CO2 emissions from road transport a widely discussed topic and constitutes a milestone towards reaching a sustainable, carbon neutral economy. This challenge is being described in various initiatives adopted in the ...
متن کاملAn Optimal G^2-Hermite Interpolation by Rational Cubic Bézier Curves
In this paper, we study a geometric G^2 Hermite interpolation by planar rational cubic Bézier curves. Two data points, two tangent vectors and two signed curvatures interpolated per each rational segment. We give the necessary and the sufficient intrinsic geometric conditions for two C^2 parametric curves to be connected with G2 continuity. Locally, the free parameters w...
متن کاملSOME RESULTS OF CONTINUITY ?f
The dynamical behavior of a map on the unit interval has been the subject of much contemporary research. In this paper, we will consider the relation between the continuity of the map cof and cof for some positive integer k, where f is a continuous map from the unit interval to itself, and ?f is a function which takes any element of the unit interval to the set of all subsequential limits o...
متن کامل