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TENSOR PRODUCTS AND SUMS OF p-HARMONIC FUNCTIONS, QUASIMINIMIZERS AND p-ADMISSIBLE WEIGHTS
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-9677-8321
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-1238-6751
2018 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 146, no 12, p. 5195-5203Article in journal (Refereed) Published
Abstract [en]

The tensor product of two p-harmonic functions is in general not p-harmonic, but we show that it is a quasiminimizer. More generally, we show that the tensor product of two quasiminimizers is a quasiminimizer. Similar results are also obtained for quasisuperminimizers and for tensor sums. This is done in weighted R-n with p-admissible weights. It is also shown that the tensor product of two p-admissible measures is p-admissible. This last result is generalized to metric spaces.

Place, publisher, year, edition, pages
AMER MATHEMATICAL SOC , 2018. Vol. 146, no 12, p. 5195-5203
Keywords [en]
Doubling measure; metric space; p-admissible weight; p-harmonic function; Poincare inequality; quasiminimizer; quasisuperminimizer; tensor product; tensor sum
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-152591DOI: 10.1090/proc/14170ISI: 000447836000017OAI: oai:DiVA.org:liu-152591DiVA, id: diva2:1262140
Note

Funding Agencies|Swedish Research Council [621-2007-6187, 621-2008-4922, 621-2014-3974, 2016-03424]

Available from: 2018-11-09 Created: 2018-11-09 Last updated: 2018-11-09

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