BELTRAMI EQUATIONS REVISITED: MARCINKIEWICZ EXPONENTS AND PAINLEVE-TYPE THEOREM

Abstract

We deal with some new results on some types of Beltrami equations. There is a new approach involving the new metric characteristics: the Marcinkiewicz exponents. Another vision is applying the Cauchy-type integral representation to such equations. One more idea is to obtain analogs of some classical theorems for such equations.

Keywords

• fractals
• non-rectifiable curves
• boundary value problem
• Riemann boundary value problem