, Volume 5, Issue 3, pp 835-845

On Integral Conditions for the General Beltrami Equations

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Abstract

Under integral restrictions on dilatations, it is proved existence theorems for the degenerate Beltrami equations with two characteristics \({{\overline {\partial}}f = \mu {{\partial f}} + \nu{\overline {\partial f}}}\) and, in particular, to the Beltrami equations of the second type \({{\overline {\partial}}f = \nu{\overline {\partial f}}}\) that play a great role in many problems of mathematical physics and to the so-called reduced Beltrami equations \({{\overline {\partial}}f = \lambda {\rm Re}\,{{\partial f}}}\) that also have significant applications.

Communicated by Lucian Beznea.