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Regularity of solutions to the quaternionic Monge-Ampère equation

2020
journal article
article
10.1007/s12220-020-00394-2
Journal
Journal of Geometric Analysis
100
Author
Kołodziej Sławomir

Sroka Marcin
Volume
30
Pages
2852-2864
ISSN
1050-6926
eISSN
1559-002X
Keywords in English

Monge-Ampere equation

pluripotential theory

subharmonic functions

Language
English
Journal language
English
Abstract in English

The regularity of solutions to the Dirichlet problem for the quaternionic Monge-Ampère equation is discussed. We prove that the solution to the Dirichlet problem is Hölder continuous under some conditions on the boundary values and the quaternionic Monge-Ampère density from Lp(Ω) for p>2. As a step towards the proof, we provide a refined version of stability for the weak solutions to this equation.

Affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki
Scopus© citations
4
dc.abstract.enThe regularity of solutions to the Dirichlet problem for the quaternionic Monge-Ampère equation is discussed. We prove that the solution to the Dirichlet problem is Hölder continuous under some conditions on the boundary values and the quaternionic Monge-Ampère density from Lp(Ω) for p>2. As a step towards the proof, we provide a refined version of stability for the weak solutions to this equation.pl
dc.affiliationWydział Matematyki i Informatyki : Instytut Matematykipl
dc.contributor.authorKołodziej, Sławomir - 129027 pl
dc.contributor.authorSroka, Marcin - 216831 pl
dc.date.accessioned2020-07-20T12:40:23Z
dc.date.available2020-07-20T12:40:23Z
dc.date.issued2020pl
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.physical2852-2864pl
dc.description.versionostateczna wersja wydawcy
dc.description.volume30pl
dc.identifier.doi10.1007/s12220-020-00394-2pl
dc.identifier.eissn1559-002Xpl
dc.identifier.issn1050-6926pl
dc.identifier.project2017/27/B/ST1/01145pl
dc.identifier.projectROD UJ / OPpl
dc.identifier.urihttps://ruj.uj.edu.pl/xmlui/handle/item/173260
dc.languageengpl
dc.language.containerengpl
dc.rightsUdzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa*
dc.rights.licenceCC-BY
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/legalcode.pl*
dc.share.typeinne
dc.subject.enMonge-Ampere equationpl
dc.subject.enpluripotential theorypl
dc.subject.ensubharmonic functionspl
dc.subtypeArticlepl
dc.titleRegularity of solutions to the quaternionic Monge-Ampère equationpl
dc.title.journalJournal of Geometric Analysispl
dc.typeJournalArticlepl
dspace.entity.typePublication
dc.abstract.enpl
The regularity of solutions to the Dirichlet problem for the quaternionic Monge-Ampère equation is discussed. We prove that the solution to the Dirichlet problem is Hölder continuous under some conditions on the boundary values and the quaternionic Monge-Ampère density from Lp(Ω) for p>2. As a step towards the proof, we provide a refined version of stability for the weak solutions to this equation.
dc.affiliationpl
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.contributor.authorpl
Kołodziej, Sławomir - 129027
dc.contributor.authorpl
Sroka, Marcin - 216831
dc.date.accessioned
2020-07-20T12:40:23Z
dc.date.available
2020-07-20T12:40:23Z
dc.date.issuedpl
2020
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.physicalpl
2852-2864
dc.description.version
ostateczna wersja wydawcy
dc.description.volumepl
30
dc.identifier.doipl
10.1007/s12220-020-00394-2
dc.identifier.eissnpl
1559-002X
dc.identifier.issnpl
1050-6926
dc.identifier.projectpl
2017/27/B/ST1/01145
dc.identifier.projectpl
ROD UJ / OP
dc.identifier.uri
https://ruj.uj.edu.pl/xmlui/handle/item/173260
dc.languagepl
eng
dc.language.containerpl
eng
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.enpl
Monge-Ampere equation
dc.subject.enpl
pluripotential theory
dc.subject.enpl
subharmonic functions
dc.subtypepl
Article
dc.titlepl
Regularity of solutions to the quaternionic Monge-Ampère equation
dc.title.journalpl
Journal of Geometric Analysis
dc.typepl
JournalArticle
dspace.entity.type
Publication
Affiliations
Wydział Matematyki i Informatyki
Kołodziej, Sławomir
Sroka, Marcin

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