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Sphericalization and p-harmonic functions on unbounded domains in Ahlfors regular spaces
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
Sun Yat Sen Univ, Peoples R China.
2019 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 474, no 2, p. 852-875Article in journal (Refereed) Published
Abstract [en]

We use sphericalization to study the Dirichlet problem, Perron solutions and boundary regularity for p-harmonic functions on unbounded sets in Ahlfors regular metric spaces. Boundary regularity for the point at infinity is given special attention. In particular, we allow for several "approach directions" towards infinity and take into account the massiveness of their complements. In 2005, Llorente-Manfredi-Wu showed that the p-harmonic measure on the upper half space R-+(n), n amp;gt;= 2, is not subadditive on null sets when p not equal 2. Using their result and spherical inversion, we create similar bounded examples in the unit ball B subset of R-n showing that the n-harmonic measure is not subadditive on null sets when n amp;gt;= 3, and neither are the p-harmonic measures in B generated by certain weights depending on p not equal 2 and n amp;gt;= 2. (C) 2019 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2019. Vol. 474, no 2, p. 852-875
Keywords [en]
Ahlfors regular metric space; Boundary regularity; Muckenhoupt A(p) weight; Perron solutions of the Dirichlet problem; p-harmonic functions and measures; Sphericalization
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-155919DOI: 10.1016/j.jmaa.2019.01.071ISI: 000461528700006OAI: oai:DiVA.org:liu-155919DiVA, id: diva2:1301552
Note

Funding Agencies|Swedish Research Council [2016-03424, 621-2014-3974]; National Natural Science Foundation of China [11701582]

Available from: 2019-04-02 Created: 2019-04-02 Last updated: 2019-04-02

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