Finite Lipschitzness of regular solutions to nonlinear Beltrami equation

Abstract

A sufficient condition providing a local finite Lipschitzness for the regular solutions of Sobolev class $W_{\mathrm{loc}}^{1,1}$ to a nonlinear Beltrami equation introduced in [Golberg A, Salimov R. Nonlinear Beltrami equation. Complex Var Elliptic Equ. 2020;65(1):6–21] is established. Some illustrating examples and preliminary results are also given.

Keywords:

• Nonlinear Beltrami equation
• ring Q-homeomorphism with respect to p-modulus
• lower Q-homeomorphism with respect to p-modulus
• tangent dilatation

AMS Subject Classifications:

• Primary: 35J60
• 30C62
• Secondary: 35B65

Acknowledgements

The first author has been supported by a fellowship of the Universities for Ukraine.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.