Search results for "Transverse measure"
showing 3 items of 3 documents
Orlicz–Sobolev extensions and measure density condition
2010
Abstract We study the extension properties of Orlicz–Sobolev functions both in Euclidean spaces and in metric measure spaces equipped with a doubling measure. We show that a set E ⊂ R satisfying a measure density condition admits a bounded linear extension operator from the trace space W 1 , Ψ ( R n ) | E to W 1 , Ψ ( R n ) . Then we show that a domain, in which the Sobolev embedding theorem or a Poincare-type inequality holds, satisfies the measure density condition. It follows that the existence of a bounded, possibly non-linear extension operator or even the surjectivity of the trace operator implies the measure density condition and hence the existence of a bounded linear extension oper…
A Riemann-Type Integral on a Measure Space
2005
In a compact Hausdorff measure space we define an integral by partitions of the unity and prove that it is nonabsolutely convergent.
The De Giorgi measure and an obstacle problem related to minimal surfaces in metric spaces
2010
Abstract We study the existence of a set with minimal perimeter that separates two disjoint sets in a metric measure space equipped with a doubling measure and supporting a Poincare inequality. A measure constructed by De Giorgi is used to state a relaxed problem, whose solution coincides with the solution to the original problem for measure theoretically thick sets. Moreover, we study properties of the De Giorgi measure on metric measure spaces and show that it is comparable to the Hausdorff measure of codimension one. We also explore the relationship between the De Giorgi measure and the variational capacity of order one. The theory of functions of bounded variation on metric spaces is us…