Spectral properties of nonassociative algebras and breaking regularity for nonlinear elliptic type PDE\MakeLowercase{s}

Tkachev, V.

doi:10.1090/spmj/1593

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.

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