Results 51 to 58 of about 448 (58)

Convexity preserving properties for Hamilton-Jacobi equations in geodesic spaces [PDF]

arXiv, 2017
We study the convexity preserving property for a class of time-dependent Hamilton-Jacobi equations in a complete geodesic space. Assuming that the Hamiltonian is nondecreasing, we show that in a Busemann space the unique metric viscosity solution preserves the geodesic convexity of the initial value at any time.
arxiv  

The Choquet and Kellogg properties for the fine topology when $p=1$ in metric spaces [PDF]

arXiv, 2017
In the setting of a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we prove the fine Kellogg property, the quasi-Lindel\"of principle, and the Choquet property for the fine topology in the case $p=1$.
arxiv  

Approximation of BV by SBV functions in metric spaces [PDF]

arXiv, 2018
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we show that functions of bounded variation (BV functions) can be approximated in the strict sense and pointwise uniformly by special functions of bounded variation, without adding significant jumps.
arxiv  

Besicovitch and doubling type properties in metric spaces [PDF]

arXiv, 2019
We explore the relationship in metric spaces between different properties related to the Besicovitch covering theorem, and also consider weak versions of doubling, in connection to the non-uniqueness of centers and radii in arbitrary metric spaces.
arxiv  

Metric currents and polylipschitz forms [PDF]

arXiv, 2019
We construct, for a locally compact metric space $X$, a space of polylipschitz forms $\bar\Gamma^*_c(X)$, which is a pre-dual for the space of metric currents of $\mathscr{D}_*(X)$ Ambrosio and Kirchheim. These polylipschitz forms may be seen as a substitute of differential forms in the metric setting.
arxiv  

A note on metric-measure spaces supporting Poincaré inequalities [PDF]

arXiv, 2019
Using a method of Korobenko, Maldonado and Rios we show a new characterization of doubling metric-measure spaces supporting Poincar\'e inequalities without assuming a priori that the measure is doubling.
arxiv  

Boundedness properties of modified averaging operators and geometrically doubling metric spaces

We characterize the geometrically doubling condition of a metric space in terms of the uniform $L^1$-boundedness of superaveraging operators, where uniform refers to the existence of bounds independent of the measure being considered.Comment: 9 pp. arXiv
Aldaz, J. M., Caldera, A.
core  

A modified proximal contraction principle with applications to variational inequality problems

In this paper, we introduce the notions of proximally completeness, proximally closedness and proximally continuity and utilize the same to prove a result on existence and uniqueness of best proximity points in the setting of metric space (not ...
Alam, Aftab
core