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Статья «SPECTRAL PROPERTIES OF NON ASSOCIATI VE ALGEBRAS AND BREAKING REGULARITY FOR NONLINEAR ELLIPTIC TYPE PDES, "Алгебра и анализ"»

Авторы:
  • TKACHEV V. G.1
стр. 51-74
Платно
1 Linkoping University
  • SDI: 007.001.0234-0852.2019.031.002.2
Ключевые слова:
  • viscosity solutions
  • elliptic type PDEs
  • compositions algebras
Аннотация:
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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