On the existence of solutions of quasilinear Beltrami equations with two characteristics
O.P. Dovhopiatyi, E.A. Sevost'yanov
TL;DR
This paper investigates the existence of solutions to quasilinear Beltrami equations with two complex characteristics, establishing conditions for homeomorphic and continuous ACL solutions with specific regularity properties.
Contribution
It provides new theorems on the existence of homeomorphic and continuous ACL solutions under certain conditions on the complex coefficients.
Findings
Existence of homeomorphic ACL solutions under specific coefficient conditions
Existence of continuous ACL solutions with logarithmic Hölder continuity
Conditions for solutions to quasilinear Beltrami equations with two characteristics
Abstract
We study Beltrami-type equations with two given complex characteristics. Under certain conditions on the complex coefficients, we obtained theorems on the existence of homeomorphic -solutions of this equation. In addition, for some relatively weak conditions, we obtained theorems on the existence of the corresponding continuous -solutions that are loga -rith\-mi\-cally H\"{o}lder in a given domain.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Differential Equations and Boundary Problems