- PII
- 10.31857/S2686954324010025-1
- DOI
- 10.31857/S2686954324010025
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 515 / Issue number 1
- Pages
- 11-17
- Abstract
- We consider a system of second order semi-linear elliptic equations in a multidimensional domain, the boundary of which is arbitrarily curved and is contained in a narrow layer along the unperturbed boundary. On the curve boundary we impose the Dirichlet or Neumann condition. In the case of the Neumann condition, on the structure of curving we additionally impose rather natural and weak conditions. Under such conditions we show that the homogenized problem is for the same system of equations in the unperturbed problem with the boundary condition of the same kind. The main result are - and L-operator estimates.
- Keywords
- осциллирующая граница условие Дирихле условие Неймана операторная оценка
- Date of publication
- 15.11.2024
- Year of publication
- 2024
- Number of purchasers
- 0
- Views
- 53
References
- 1. Sanchez-Palencia E.. Non-homogeneous media and vibration theory. New York: Springer, 1980. 409 pp.
- 2. Олейник О.А., Иосифьян Г.А., Шамаев А.С. Математические задачи теории сильно неоднородных упругих сред. М.: Изд-во МГУ, 1990. 312 с.
- 3. Беляев А.Г., Михеев А.Г., Шамаев А.С. // Ж. вычисл. матем. матем. физ. 1992. Т. 32. № 8. С. 1258–1272.
- 4. Чечкин Г.А., Акимова Е.А., Назаров С.А. // Доклады РАН. 2001. Т. 380. № 4. С. 439–442.
- 5. Грушин В.В., Доброхотов С.Ю. // Матем. заметки. 2014. Т. 95. № 3. С. 359–375.
- 6. Козлов В.А., Назаров С.А. // Алг. ан. 2010. Т. 22. № 6. С. 127–184.
- 7. Пастухова С.Е. // Дифф. уравн. 2001. Т. 37. № 9. С. 1216–1222.
- 8. Amirat Y., Bodart O., Chechkin G.A., Piatnitski A.L. // Stoch. Process. Appl. 2011. Т. 121. № 1. С. 1–23.
- 9. Arrieta J., Brushi S. // Discr. Cont. Dyn. Syst. Ser. B. 2010. Vol. 14. No. 2. P. 327–351.
- 10. Chechkin G.A., Friedman A., Piatnitski A.L. // J. Math. Anal. Appl. 1999. Vol. 231. No. 1. P. 213–234.
- 11. Jäger W., Mikelić A. // Comm. Math. Phys. 2003. Vol. 232. No. 3. P. 429–455.
- 12. Myong-Hwan Ri // Preprint: arXiv: 1311.0977. 2013.
- 13. Neuss N., Neuss-Radu M., Mikelić A. // Applic. Anal. 2006. Vol. 85. No. 5. P. 479–502.
- 14. Borisov D., Cardone G., Faella L., Perugia C. // J. Diff. Equat. 2013. Vol. 255. No. 12. P. 4378–4402.
- 15. Борисов Д.И. // Пробл. матем. ан. 2022. Вып. 116. С. 69–84.
