Hh Older Quasicontinuity of Sobolev Functions on Metric Spaces
نویسنده
چکیده
We prove that every Sobolev function de ned on a metric space coincides with a Holder continuous function outside a set of small Hausdor content or capacity. Moreover, the Holder continuous function can be chosen so that it approximates the given function in the Sobolev norm. This is a generalization of a result of Mal y [Ma1] to the Sobolev spaces on metric spaces [H1].
منابع مشابه
Quasiopen and p-Path Open Sets, and Characterizations of Quasicontinuity
In this paper we give various characterizations of quasiopen sets and quasicontinuous functions on metric spaces. For complete metric spaces equipped with a doubling measure supporting a p-Poincaré inequality we show that quasiopen and p-path open sets coincide. Under the same assumptions we show that all Newton-Sobolev functions on quasiopen sets are quasicontinuous.
متن کاملTwo-microlocal Spaces, Local Norms, and Weighted Spaces
We generalize the two-microlocal spaces of Bony to a Triebel-Lizorkin setting, which includes HH older and general Sobolev type spaces as special cases, and prove that these spaces can be characterized by size estimates on wavelet coeecients. Using this characterization we then prove two alternative characterizations of the new spaces, where the rst one involves local norms and the second one r...
متن کاملAnalysis and Pde on Metric Measure Spaces: Sobolev Functions and Viscosity Solutions
ANALYSIS AND PDE ON METRIC MEASURE SPACES: SOBOLEV FUNCTIONS AND VISCOSITY SOLUTIONS Xiaodan Zhou, PhD University of Pittsburgh, 2016 We study analysis and partial differential equations on metric measure spaces by investigating the properties of Sobolev functions or Sobolev mappings and studying the viscosity solutions to some partial differential equations. This manuscript consists of two par...
متن کاملFixed Point Theorems on Complete Quasi Metric Spaces Via C-class and A-Class Functions
In this paper, we present some fixed point theorems for single valued mappings on $K$-complete, $M$-complete and Symth complete quasi metric spaces. Here, for contractive condition, we consider some altering distance functions together with functions belonging to $C$-class and $A$-class. At the same time, we will consider two different type $M$ functions in contractive conditions because the qu...
متن کاملOn extensions of Sobolev functions defined on regular subsets of metric measure spaces
We characterize the restrictions of first order Sobolev functions to regular subsets of a homogeneous metric space and prove the existence of the corresponding linear extension operator. Let (X, d, µ) be a metric space (X, d) equipped with a Borel measure µ, which is non-negative and outer regular, and is finite on every bounded subset. In this paper we describe the restrictions of first order ...
متن کامل