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Pasting Lemmas and Characterizations of Boundary Regularity for Quasiminimizers
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9677-8321
University Helsinki, Department Math, FI-00014 Helsinki, Finland .
2009 (English)In: RESULTS IN MATHEMATICS, ISSN 1422-6383, Vol. 55, no 3-4, 265-279 p.Article in journal (Refereed) Published
Abstract [en]

Quasiharmonic functions correspond to p-harmonic functions when minimizers of the p-Dirichlet integral are replaced by quasiminimizers. In this paper, boundary regularity for quasiminimizers is characterized in several ways; in particular it is shown that regularity is a local property of the boundary. For these characterizations we employ a version of the so called pasting lemma; this is a useful tool in the theory of superharmonic functions and our version extends the classical pasting lemma to quasisuperharmonic functions and quasisuperminimizers. The results are obtained for metric measure spaces, but they are new also in the Euclidean spaces.

Place, publisher, year, edition, pages
2009. Vol. 55, no 3-4, 265-279 p.
Keyword [en]
Boundary regularity, characterization, local property, metric space, nonlinear, pasting lemma, p-harmonic, potential theory, quasiharmonic, quasiminimizer, quasisubharmonic, quasisubminimizer, quasisuperharmonic, quasisuperminimizer
National Category
URN: urn:nbn:se:liu:diva-52762DOI: 10.1007/s00025-009-0437-2OAI: diva2:285493
Available from: 2010-01-12 Created: 2010-01-12 Last updated: 2013-12-17

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Björn, Anders
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Applied MathematicsThe Institute of Technology

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