Beltrami equation with coefficient in Sobolev and Besov spaces

Abstract

Our goal in this work is to present some function spaces on the complex plane $\C$, $X(\C)$, for which the quasiregular solutions of the Beltrami equation, $\bar{\partial }f(z)=\mu (z)\partial f(z)$, have first derivatives locally in $X(\C)$, provided that the Beltrami coefficient $\mu$ belongs to $X(\C)$.

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• Non uniform rotating vortices and periodic orbits for the two-dimensional Euler Equations
• Characterization for stability in planar conductivities
• Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale
• Weighted Sobolev estimates of the truncated Beurling operator