Geodesic
Operator estimates for the averaging of the Riemann-Hilbert problem for the Beltrami equation with a locally periodic coefficient
Daghestan Electronic Mathematical Reports, Tome 16 (2021), pp. 51-61

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Local characteristics of mathematical models of strongly inhomogeneous media are usually described by functions of the form $a(\varepsilon^{-1} x)$, $b(x,\varepsilon^{-1} x)$, $c(\varepsilon^{-1} x,\delta^{-1} x)$, $d(\varepsilon^{-1} x,\delta^{-1} x,\gamma^{-1} x)$, etc., where $\varepsilon$, $\delta$, $\gamma,\ldots>0$ — small parameters, while functions $a$, $b$, $c$, $d$, $\ldots$ have an ordered structure (for example, they are periodic in variables $y=\varepsilon^{-1} x$, $z=\delta^{-1} x$, etc.). Consequently, the corresponding mathematical models are differential equations with rapidly oscillating coefficients. This work is devoted to estimates of the averaging error. We study the generalized Beltrami equation with a locally periodic coefficient $\mu(x,\varepsilon^{-1} x)$.
Keywords: Beltrami equation, averaging, asymptotic methods. 
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     author = {M. M. Sirazhudinov and L. M. Dzhabrailova},
     title = {Operator estimates for the averaging of the {Riemann-Hilbert} problem for the {Beltrami} equation with a locally periodic coefficient},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {51--61},
     publisher = {mathdoc},
     volume = {16},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2021_16_a3/}
}
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M. M. Sirazhudinov; L. M. Dzhabrailova. Operator estimates for the averaging of the Riemann-Hilbert problem for the Beltrami equation with a locally periodic coefficient. Daghestan Electronic Mathematical Reports, Tome 16 (2021), pp. 51-61. http://geodesic.mathdoc.fr/item/DEMR_2021_16_a3/