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Differential tests for plurisubharmonic functions and Koch curves
complex Monge-Ampère operator
Hausdorff dimension
Koch curve
strictly plurisubharmonic function
differential test
viscosity
We study minimum sets of singular plurisubharmonic functions and their relation to upper contact sets. In particular we develop an algorithm checking when a naturally parametrized curve is such a minimum set. The case of Koch curves is studied in detail. We also study the size of the set of upper non-contact points. We show that this set is always of Lebesgue measure zero thus answering an open problem in the viscosity approach to the complex Monge-Ampère equation. Finally, we prove that similarly to the case of convex functions, strictly plurisubharmonic lower tests yield existence of upper tests with a control on the opening.
dc.abstract.en | We study minimum sets of singular plurisubharmonic functions and their relation to upper contact sets. In particular we develop an algorithm checking when a naturally parametrized curve is such a minimum set. The case of Koch curves is studied in detail. We also study the size of the set of upper non-contact points. We show that this set is always of Lebesgue measure zero thus answering an open problem in the viscosity approach to the complex Monge-Ampère equation. Finally, we prove that similarly to the case of convex functions, strictly plurisubharmonic lower tests yield existence of upper tests with a control on the opening. | pl |
dc.affiliation | Wydział Matematyki i Informatyki : Instytut Matematyki | pl |
dc.contributor.author | Dinew, Sławomir - 200069 | pl |
dc.contributor.author | Dinew, Żywomir - 147962 | pl |
dc.date.accessioned | 2019-04-10T06:48:27Z | |
dc.date.available | 2019-04-10T06:48:27Z | |
dc.date.issued | 2019 | pl |
dc.date.openaccess | 0 | |
dc.description.accesstime | w momencie opublikowania | |
dc.description.number | 3 | pl |
dc.description.physical | 381-400 | pl |
dc.description.version | ostateczna wersja wydawcy | |
dc.description.volume | 50 | pl |
dc.identifier.doi | 10.1007/s11118-018-9686-6 | pl |
dc.identifier.eissn | 1572-929X | pl |
dc.identifier.issn | 0926-2601 | pl |
dc.identifier.project | NCN grant 2013/11/D/ST1/02599 | pl |
dc.identifier.project | Ideas Plus 0001/ID3/2014/63 | pl |
dc.identifier.project | ROD UJ / OP | pl |
dc.identifier.uri | https://ruj.uj.edu.pl/xmlui/handle/item/72632 | |
dc.language | eng | pl |
dc.language.container | eng | pl |
dc.rights | Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa | * |
dc.rights.licence | CC-BY | |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/legalcode.pl | * |
dc.share.type | inne | |
dc.subject.en | complex Monge-Ampère operator | pl |
dc.subject.en | Hausdorff dimension | pl |
dc.subject.en | Koch curve | pl |
dc.subject.en | strictly plurisubharmonic function | pl |
dc.subject.en | differential test | pl |
dc.subject.en | viscosity | pl |
dc.subtype | Article | pl |
dc.title | Differential tests for plurisubharmonic functions and Koch curves | pl |
dc.title.journal | Potential Analysis | pl |
dc.type | JournalArticle | pl |
dspace.entity.type | Publication |
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