Spectral properties of nonassociative algebras and breaking regularity for nonlinear elliptic type PDE\MakeLowercase{s}
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- by V. G. Tkachev
- St. Petersburg Math. J. 31 (2020), 223-240
- DOI: https://doi.org/10.1090/spmj/1593
- Published electronically: February 4, 2020
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Abstract:
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? Our aim in the paper is twofold. First, 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. Second, to define an appropriate algebraic formalism, which makes the analytic part of the construction of nonclassical solutions more transparent.References
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Bibliographic Information
- V. G. Tkachev
- Affiliation: Department of Mathematics, Linköping University, SE-581 83, Sweden
- MR Author ID: 246080
- Email: vladimir.tkatjev@liu.se
- Received by editor(s): November 12, 2018
- Published electronically: February 4, 2020
- © Copyright 2020 American Mathematical Society
- Journal: St. Petersburg Math. J. 31 (2020), 223-240
- MSC (2010): Primary 53A04; Secondary 52A40, 52A10
- DOI: https://doi.org/10.1090/spmj/1593
- MathSciNet review: 3937497
Dedicated: Dedicated to V. G. Maz’ya on the occasion of his $80$th birthday