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

• Autorzy: Heikki Hakkarainen , Juha Kinnunen , Panu Lahti , Pekka Lehtelä
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

calculus of variations; functionals of linear growth; relaxation; functions of bounded variation; analysis on metric measure spaces

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2016
• Tom: 4
• Numer: 1

Daty

otrzymano

2016-04-20

zaakceptowano

2016-09-02

online

2016-11-10

Twórcy

autor

Heikki Hakkarainen

• Department of Mathematical Sciences, P.O. Box 3000, FI-90014 University of Oulu, Finland

autor

Juha Kinnunen

• Aalto University, School of Science, Department of Mathematics, P.O. Box 11100, FI-00076 Aalto, Finland

autor

Panu Lahti

• Aalto University, School of Science, Department of Mathematics, P.O. Box 11100, FI-00076 Aalto, Finland

autor

Pekka Lehtelä

• Aalto University, School of Science, Department of Mathematics, P.O. Box 11100, FI-00076 Aalto, Finland

Identyfikatory

DOI

10.1515/agms-2016-0013