Enviar artigo por via de e-mail Integral Identity and Estimate of the Deviation of Approximate Solutions of a Biharmonic Obstacle Problem
- Autores: Besov K.O.1,2
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Afiliações:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Institute of Mathematics and Mathematical Modeling
- Edição: Volume 63, Nº 3 (2023)
- Páginas: 351-354
- Seção: Optimal control
- URL: https://ogarev-online.ru/0044-4669/article/view/134299
- DOI: https://doi.org/10.31857/S0044466923030031
- EDN: https://elibrary.ru/DXXEPD
- ID: 134299
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Texto integral
Resumo
We show that the integral identity obtained by D.E. Apushkinskaya and S.I. Repin (2020) for approximate solutions of the biharmonic obstacle problem that satisfy a pointwise constraint on the second divergence is valid for arbitrary approximate solutions. Using this result, we obtain a new estimate for the deviation of approximate solutions from exact ones in the case when the approximate solutions do not satisfy the pointwise constraint on the second divergence.
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Sobre autores
K. Besov
Steklov Mathematical Institute of Russian Academy of Sciences; Institute of Mathematics and Mathematical Modeling
Autor responsável pela correspondência
Email: kbesov@mi-ras.ru
119991, Moscow, Russia; 050010, Almaty, Kazakhstan
Bibliografia
- Апушкинская Д.Е., Репин С.И. Бигармоническая задача с препятствием: гарантированные и вычисляемые оценки ошибок для приближенных решений // Ж. вычисл. матем. и матем. физ. 2020. Т. 60. № 11. С. 1881–1897.
- Caffarelli L.A., Friedman A. The obstacle problem for the biharmonic operator // Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 1979. V. 6. P. 151–184.
- Frehse J. On the regularity of the solution of the biharmonic variational inequality // Manuscr. Math. 1973. V. 9. P. 91–103.
- Стейн И.М. Сингулярные интегралы и дифференциальные свойства функций. М.: Мир, 1973.
- Scherfgen D. Integral calculator. https://www.integral-calculator.com.
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