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Integral Identity and Estimate of the Deviation of Approximate Solutions of a Biharmonic Obstacle Problem
- Authors: Besov K.O.1,2
-
Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Institute of Mathematics and Mathematical Modeling
- Issue: Vol 63, No 3 (2023)
- Pages: 351-354
- Section: Optimal control
- URL: https://rjpbr.com/0044-4669/article/view/664874
- DOI: https://doi.org/10.31857/S0044466923030031
- EDN: https://elibrary.ru/DXXEPD
- ID: 664874
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Abstract
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.
About the authors
K. O. Besov
Steklov Mathematical Institute of Russian Academy of Sciences; Institute of Mathematics and Mathematical Modeling
Author for correspondence.
Email: kbesov@mi-ras.ru
119991, Moscow, Russia; 050010, Almaty, Kazakhstan
References
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- 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.
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