Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 551-560

SOBOLEV SPACES, FINE GRADIENTS AND QUASICONTINUITY ON QUASIOPEN SETS

Anders Björn, Jana Björn and Visa Latvala

Linköping University, Department of Mathematics
SE-581 83 Linköping, Sweden; anders.bjorn 'at' liu.se

Linköping University, Department of Mathematics
SE-581 83 Linköping, Sweden; jana.bjorn 'at' liu.se

University of Eastern Finland, Department of Physics and Mathematics
P.O. Box 111, FI-80101 Joensuu, Finland; visa.latvala 'at' uef.fi

Abstract. We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space X equipped with a doubling measure supporting a p-Poincaré inequality with 1 < p < ∞, and connect them to the Sobolev theory in Rⁿ.

2010 Mathematics Subject Classification: Primary 46E35; Secondary 30L99, 31C40, 31C45, 31E05.

Key words: Fine gradient, fine topology, metric space, minimal upper gradient, Newtonian space, quasicontinuous, quasiopen, Sobolev space.

Reference to this article: A. Björn, J. Björn and V. Latvala: Sobolev spaces, fine gradients and quasicontinuity on quasiopen sets. Ann. Acad. Sci. Fenn. Math. 41 (2016), 551-560.

Full document as PDF file

doi:10.5186/aasfm.2016.4130