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Journal of Mathematical Sciences

, Volume 224, Issue 5, pp 744–763 | Cite as

Homogenization Estimates in the Riemann–Hilbert Problem for the General Beltrami Equation on the Plane

  • S. E. PastukhovaEmail author
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We study homogenization for the Beltrami equation \( {A}_{\varepsilon }{u}_{\varepsilon}\equiv {\partial}_{\overline{z}}{u}_{\varepsilon }+{\mu}^{\varepsilon }{\partial}_z{u}_{\varepsilon }+{\nu}^{\varepsilon}\overline{\partial_z{u}_{\varepsilon }}=f \) with measurable ε-periodic coefficients μ ε and ν ε , where ε is a small parameter. The coefficients of the equation satisfy the uniform ellipticity condition. The equation is considered in a bounded domain Ω of the complex plane with the Riemann–Hilbert condition on the boundary ∂Ω. For the resolvent \( {A}_{\varepsilon}^{-1} \) of this boundary value problem we obtain an approximation in the operator norm of the Sobolev space W 1,2(Ω) with approximation error of order O(\( \sqrt{\varepsilon } \)).

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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Moscow Technological University (MIREA)MoscowRussia

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