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Spectral properties of nonassociative algebras and breaking regularity for nonlinear elliptic type PDEs
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-8422-6140
2019 (English)In: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 31, no 2, p. 255-278Article in journal (Refereed) Published
Abstract [en]

In this paper, we address the following question: Why certain nonassociative algebra structures emerge in the regularity theory of elliptic type PDEs and also in constructing nonclassical and singular solutions? The aim of the paper is twofold. Firstly, to give a survey of diverse examples on nonregular solutions to elliptic PDEs with emphasis on recent results on nonclassical solutions to fully nonlinear equations. Secondly, to define an appropriate algebraic formalism which makes the analytic part of the construction of nonclassical solutions more transparent.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2019. Vol. 31, no 2, p. 255-278
Keywords [en]
Ellitpic type PDEs, Nonassociative algebras, Idempotents
National Category
Mathematical Analysis Algebra and Logic
Identifiers
URN: urn:nbn:se:liu:diva-154520OAI: oai:DiVA.org:liu-154520DiVA, id: diva2:1290328
Available from: 2019-02-20 Created: 2019-02-20 Last updated: 2019-03-25Bibliographically approved

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Tkachev, Vladimir

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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
  • rtf