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Minima of quasisuperminimizers
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
Aalto University, Finland.
2017 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 155, 264-284 p.Article in journal (Refereed) Published
Abstract [en]

We show that, unlike minima of superharmonic functions which are again superharmonic, the same property fails for Q-quasisuperminimizers. More precisely, if u(i) is a Q(i)-quasisuperminimizer, i = 1,2, where 1 amp;lt; Q(1) amp;lt; Q(2), then u = min{u(1), u(2)} is a Q-quasisuperminimizer, but there is an increase in the optimal quasisuperminimizing constant Q. We provide the first examples of this phenomenon, i.e. that Q amp;gt; Q(2). In addition to lower bounds for the optimal quasisuperminimizing constant of u we also improve upon the earlier upper bounds due to Kinnunen and Martio. Moreover, our lower and upper bounds turn out to be quite close. We also study a similar phenomenon in pasting lemmas for quasisuperminimizers, where Q = Q(1)Q(2) turns out to be optimal, and provide results on exact quasiminimizing constants of piecewise linear functions on the real line, which can serve as approximations of more general quasiminimizers. (C) 2017 Elsevier Ltd. All rights reserved.

Place, publisher, year, edition, pages
PERGAMON-ELSEVIER SCIENCE LTD , 2017. Vol. 155, 264-284 p.
Keyword [en]
Metric space; Nonlinear potential theory; Pasting lemma; Quasiminimizer; Quasisuperharmonic function; Quasisuperminimizer
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-137602DOI: 10.1016/j.na.2017.02.003ISI: 000400231200015OAI: oai:DiVA.org:liu-137602DiVA: diva2:1097369
Note

Funding Agencies|Swedish Research Council [621-2007-6187, 621-2008-4922, 621-2011-3139, 621-2014-3974, 2016-03424]; Academy of Finland [250403]

Available from: 2017-05-22 Created: 2017-05-22 Last updated: 2017-05-22

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