2019
Том 71
№ 11

All Issues

Yakubov E.

Articles: 1
Article (English)

On the theory of the Beltrami equation

Ryazanov V. I., Srebro U., Yakubov E.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 11. - pp. 1571–1583

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.