Operator L 2-Estimates for Two-Dimensional Problems with Rapidly Alternating Boundary Conditions
Borisov D.I. Konyrkulzhaeva M.N.
October 2022Springer
Journal of Mathematical Sciences (United States)
2022#267Issue 3319 - 337 pp.
We consider a second order operator with complex coefficients in a plane domain with the Dirichlet boundary condition and the nonlinear third kind boundary condition nonperiodically alternating on some boundary component. We study the case where the homogenization leads in the limit to the Dirichlet boundary condition. We prove order sharp estimates for the W21- and L2-norms of the difference of solutions to the perturbed and homogenized problems. The estimates are uniform with respect to the L2-norm of the right-hand side of the equation of the problem.
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Institute of Mathematics, UFRC RAS, 112, Chernyshevskii St, Ufa, 450008, Russian Federation
M. Akhmula Bashkir State Pedagogical University, 3a, October Revolution St, Ufa, 450000, Russian Federation
International Information Technology University, 8, Manas St, Almaty, 050000, Kazakhstan
Institute of Mathematics
M. Akhmula Bashkir State Pedagogical University
International Information Technology University
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