Results 21 to 30 of about 211 (33)

Lusin-type theorems for Cheeger derivatives on metric measure spaces

, 2015
A theorem of Lusin states that every Borel function on $R$ is equal almost everywhere to the derivative of a continuous function. This result was later generalized to $R^n$ in works of Alberti and Moonens-Pfeffer. In this note, we prove direct analogs of
David, Guy C.
core   +2 more sources

Sobolev spaces, fine gradients and quasicontinuity on quasiopen sets

, 2015
We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space equipped with a doubling measure supporting a p-Poincar\'e inequality with ...
Björn, Anders, Björn, Jana, Latvala, Visa   +2 more
core   +1 more source

Sphericalization and p-harmonic functions on unbounded domains in Ahlfors regular metric spaces

, 2018
We use sphericalization to study the Dirichlet problem, Perron solutions and boundary regularity for p-harmonic functions on unbounded sets in Ahlfors regular metric spaces. Boundary regularity for the point at infinity is given special attention.
Bjorn, Anders, Bjorn, Jana, Li, Xining
core   +1 more source

Capacities and 1-strict subsets in metric spaces

, 2019
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.
Lahti, Panu
core   +1 more source

Vector-valued non-homogeneous Tb theorem on metric measure spaces [PDF]

, 2010
We prove a vector-valued non-homogeneous Tb theorem on certain quasimetric spaces equipped with what we call an upper doubling measure. Essentially, we merge recent techniques from the domain and range side of things, achieving a Tb theorem which is ...
Martikainen, Henri
core  

Poincar\'e inequalities and Newtonian Sobolev functions on noncomplete metric spaces

, 2019
Let $X$ be a noncomplete metric space satisfying the usual (local) assumptions of a doubling property and a Poincar\'e inequality. We study extensions of Newtonian Sobolev functions to the completion $\widehat{X}$ of $X$ and use them to obtain several ...
Björn, Anders, Björn, Jana
core   +1 more source

Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices

, 2012
Properties of first-order Sobolev-type spaces on abstract metric measure spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are investigated.
Malý, Lukáš
core   +1 more source

Geometric characterization of generalized Hajłasz-Sobolev embedding domains

Advances in Nonlinear Analysis
In this article, the authors study the embedding properties of Hajłasz-Sobolev spaces with generalized smoothness on Euclidean domains, whose regularity is described via a smoothness weight function ϕ:[0,∞)→[0,∞)\phi :\left[0,\infty )\to \left[0,\infty ).
Li Ziwei, Yang Dachun, Yuan Wen
doaj   +1 more source

Qualitative Lipschitz to bi-Lipschitz decomposition

Analysis and Geometry in Metric Spaces
We prove that any Lipschitz map that satisfies a condition inspired by the work of G. David may be decomposed into countably many bi-Lipschitz pieces.
Bate David
doaj   +1 more source

Cheeger's differentiation theorem via the multilinear Kakeya inequality

, 2019
Suppose that $(X,d,\mu)$ is a metric measure space of finite Hausdorff dimension and that, for every Lipschitz $f \colon X \to \mathbb R$, $\operatorname{Lip}(f,\cdot)$ is dominated by every upper gradient of $f$.
Bate, David, Kangasniemi, Ilmari, Orponen, Tuomas   +2 more
core