## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

DCDS

We study the properties of the transport density measure
in the Monge-Kantorovich
optimal mass transport problem in the presence of so-called Dirichlet
constraint, i.e. when some
closed set is given
along which the cost of transportation is zero. The Hausdorff dimension
estimates, as well as summability and higher regularity properties
of the transport density are studied. The uniqueness of the
transport density is proven in the case when the masses to be transported
are represented by measures absolutely continuous with respect
to the Lebesgue measure.

DCDS

We prove that every one-dimensional real Ambrosio-Kirchheim current with
zero boundary (i.e. a cycle) in a lot of reasonable spaces (including all finite-dimensional normed spaces)
can be represented by a Lipschitz curve parameterized over the real line through a suitable limit
of Cesàro means of this curve over a subsequence of symmetric bounded intervals (viewed as currents). It is further shown that in such spaces,
if a
cycle is indecomposable, i.e. does not contain ``nontrivial'' subcycles, then it can be represented
again by a Lipschitz curve parameterized over the real line through a limit
of Cesàro means of this curve over every sequence of symmetric bounded intervals, that is, in other words, such a cycle
is a solenoid.

keywords:
Ambrosio-Kirchheim currents
,
solenoids.
,
metric currents
,
Lipschitz curves
,
Normal currents

## Year of publication

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