2017
Том 69
№ 7

# On the theory of the Beltrami equation

Abstract

We study ring homeomorphisms and, on this basis, obtain a series of theorems on the existence of the so-called ring solutions for degenerate Beltrami equations. A general statement on the existence of solutions for the Beltrami equations that extends earlier results is formulated. In particular, we give new existence criteria for homeomorphic solutions $f$ of the class $W^{1, 1}_{\text{loc}}$ with f −1 ∈ $f^{—1} \in W^{1, 2}_{\text{loc}}$ in terms of tangential dilatations and functions of finite mean oscillation. The ring solutions also satisfy additional capacity inequalities.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 11, pp 1786-1798.

Citation Example: Ryazanov V. I., Srebro U., Yakubov E. On the theory of the Beltrami equation // Ukr. Mat. Zh. - 2006. - 58, № 11. - pp. 1571–1583.

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