O gipersingulyarnykh operatorakh, svyazannykh s peridinamikoy

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Resumo

For a hypersingular integral operator of the Calderón–Zygmund type associated with problems of peridynamics, we find a Hilbert space that is taken by this operator to the space of square integrable periodic functions.

Sobre autores

Sh. Alimov

National University of Uzbekistan

Email: sh_alimov@mail.ru
Tashkent, 100174, Uzbekistan

Sh. Sheraliev

Tashkent Branch, Lomonosov Moscow State University

Autor responsável pela correspondência
Email: shuhrat2500@mail.ru
Tashkent, 100060, Uzbekistan

Bibliografia

  1. Silling S.A. Reformulation of elasticity theory for discontinuities and long-range forces // J. Mech. Phys. Solids. 2000. V. 48. № 1. P. 175-209.
  2. Calderon A.P., Zygmund A. On the existence of certain singular integrals // Acta Math. 1952. V. 88. P. 85-139.
  3. Тихонов А.Н., Самарский А.А. Уравнения математической физики. М., 1999.
  4. Ильин В.А. Ядра дробного порядка // Мат. сб. 1957. Т. 41 (83). № 4. С. 459-480.
  5. Alimov Sh., Sheraliev Sh. On the solvability of the singular equation of peridynamics // Complex Variables and Elliptic Equat. 2019. V. 64. № 5. P. 873-887.
  6. Ильин В.А. Спектральная теория дифференциальных операторов. Самосопряжённые дифференциальные операторы. М., 1991.

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