2017
Том 69
№ 9

All Issues

On the boundary behavior of solutions of the Beltrami equations

Kovtonyuk D. A., Petkov I. V., Ryazanov V. I.

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Abstract

We show that every homeomorphic solution of the Beltrami equation $\overline{\partial} f = \mu \partial f$ in the Sobolev class $W^{1, 1}_{\text{loc}}$ is a so-called lower $Q$-homeomorphism with $Q(z) = K_{\mu}(z)$, where $K_{\mu}$ is a dilatation quotient of this equation. On this basis, we develop the theory of the boundary behavior and the removability of singularities of these solutions.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 8, pp 1241-1255.

Citation Example: Kovtonyuk D. A., Petkov I. V., Ryazanov V. I. On the boundary behavior of solutions of the Beltrami equations // Ukr. Mat. Zh. - 2011. - 63, № 8. - pp. 1078-1091.

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