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Эта публикация цитируется в 6 научных статьях (всего в 6 статьях)
Обзоры
Spectral properties of nonassociative algebras and breaking regularity for nonlinear elliptic type PDEs
V. G. Tkachev Department of Mathematics, Linköping University, SE-581 83, Sweden
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.
Ключевые слова:
viscosity solutions, elliptic type PDEs, compositions algebras.
Поступила в редакцию: 12.11.2018
Образец цитирования:
V. G. Tkachev, “Spectral properties of nonassociative algebras and breaking regularity for nonlinear elliptic type PDEs”, Алгебра и анализ, 31:2 (2019), 51–74; St. Petersburg Math. J., 31:2 (2019), 223–240
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1637 https://www.mathnet.ru/rus/aa/v31/i2/p51
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Страница аннотации: | 279 | PDF полного текста: | 38 | Список литературы: | 40 | Первая страница: | 13 |
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