Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Resistance Conditions and Applications

100%

Kinnunen J., Silvestre P.

Analysis and Geometry in Metric Spaces

2013

tom 1

276-294

This paper studies analytic aspects of so-called resistance conditions on metric measure spaces with a doubling measure. These conditions are weaker than the usually assumed Poincaré inequality, but however, they are sufficiently strong to imply several useful results in analysis on metric measure spaces. We show that under a perimeter resistance condition, the capacity of order one and the Hausdorff content of codimension one are comparable. Moreover, we have connections to the Sobolev inequality for compactly supported Lipschitz functions on balls as well as capacitary strong type estimates for the Hardy-Littlewood maximal function. We also consider extensions to Sobolev type inequalities with two different measures and Lorentz type estimates.

Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces

81%

Hakkarainen H., Kinnunen J., Lahti P., Lehtelä P.

Analysis and Geometry in Metric Spaces

2016

tom 4

nr 1

This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincaré inequality. Such a functional is defined via relaxation, and it defines a Radon measure on the space. For the singular part of the functional, we get the expected integral representation with respect to the variation measure. A new feature is that in the representation for the absolutely continuous part, a constant appears already in the weighted Euclidean case. As an application we show that in a variational minimization problem involving the functional, boundary values can be presented as a penalty term.

Ograniczanie wyników

2 Analysis and Geometry in Metric Spaces

2 Kinnunen J.

1 Hakkarainen H.

1 Lahti P.

1 Lehtelä P.

1 Silvestre P.

1 2016

1 2013

Wyniki wyszukiwania

Resistance Conditions and Applications

Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces