Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 531-540

LOOKING FOR COMPACTNESS IN SOBOLEV SPACES ON NONCOMPACT METRIC SPACES

Przemyslaw Górka

Warsaw University of Technology, Department of Mathematics and Information Sciences
Ul. Koszykowa 75, 00-662 Warsaw, Poland; pgorka 'at' mini.pw.edu.pl

Abstract. We study Sobolev spaces on noncompact metric measure spaces. We show compact embedding of H-invariant Sobolev spaces, where H is a subgroup of all isometries preserving the measure on the metric measure space.

2010 Mathematics Subject Classification: Primary 46E35, 30L99.

Key words: Sobolev spaces, metric measure spaces, compact embedding, Berestycki–Lions theorem, covering lemma, isometries preserving measure.

Reference to this article: P. Górka: Looking for compactness in Sobolev spaces on noncompact metric spaces. Ann. Acad. Sci. Fenn. Math. 43 (2018), 531-540.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4332