Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices
2013 (English)In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 38, no 2, 727-745 p.Article in journal (Refereed) Published
Properties of first-order Sobolev-type spaces on abstract metric measure spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are investigated. The set of all weak upper gradients of a Newtonian function is of particular interest. Existence of minimal weak upper gradients in this general setting is proven and corresponding representation formulae are given. Furthermore, the connection between pointwise convergence of a sequence of Newtonian functions and its convergence in norm is studied.
Place, publisher, year, edition, pages
Suomalainen Tiedeakatemia , 2013. Vol. 38, no 2, 727-745 p.
Newtonian space, upper gradient, weak upper gradient, Banach function lattice, quasi-normed space, metric measure space
IdentifiersURN: urn:nbn:se:liu:diva-79165DOI: 10.5186/aasfm.2013.3831ISI: 000322091900020OAI: oai:DiVA.org:liu-79165DiVA: diva2:538661