Estimates of Homogenization for the Beltrami Equation

Аннотация

We study the homogenization of the Riemann–Hilbert boundary value problem for the Beltrami equation with an oscillating ε-periodic coefficient, where ε > 0 is a small parameter. The homogenized problem has a similar form, but with a constant coefficient. We prove error estimates of homogenization in the L₂- and W₂¹ -norms of order \( O\left(\sqrt{\varepsilon}\right) \). Bibliography: 9 titles.