Integral Identity and Estimate of the Deviation of Approximate Solutions of a Biharmonic Obstacle Problem

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详细

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.

作者简介

K. Besov

Steklov Mathematical Institute of Russian Academy of Sciences; Institute of Mathematics and Mathematical Modeling

编辑信件的主要联系方式.
Email: kbesov@mi-ras.ru
119991, Moscow, Russia; 050010, Almaty, Kazakhstan

参考

  1. 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.
  2. 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.
  3. Frehse J. On the regularity of the solution of the biharmonic variational inequality // Manuscr. Math. 1973. V. 9. P. 91–103.
  4. Стейн И.М. Сингулярные интегралы и дифференциальные свойства функций. М.: Мир, 1973.
  5. Scherfgen D. Integral calculator. https://www.integral-calculator.com.

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