We obtain improved regularity of homeomorphic solutions of the reduced Beltrami equation, as compared to the standard Beltrami equation. Such an improvement is not possible in terms of Hölder or Sobolev regularity; instead, our results concern the generalized variation of restrictions to lines. Specifically, we prove that the restriction to any line segment has finite p-variation for all p > 1 ...

Abstract. The paper concerns numerical algorithms for solving the Beltrami equation fz̄(z) = μ(z)fz(z) for a compactly supported μ. First, we study an efficient algorithm that has been proposed in the literature, and present its rigorous justification. We then propose a different scheme for solving the Beltrami equation which has a comparable speed and accuracy, but has the virtue of a greater s...

We provide estimates for the Hölder exponent of solutions to the Beltrami equation ∂f = μ∂f + ν∂f , where the Beltrami coefficients μ, ν satisfy ‖|μ|+ |ν|‖∞ < 1 and =(ν) = 0. Our estimates depend on the arguments of the Beltrami coefficients as well as on their moduli. Furthermore, we exhibit a class of mappings of the “angular stretching” type, on which our estimates are actually attained.

The two-fluid model of a plasma describes the strong coupling between the magnetic and the fluid aspects of the plasma. The Beltrami condition which demands alignment of vortices and flows becomes a system of simultaneous equations in the magnetic field and the flow velocity. Combining these equations yields the double curl Beltrami equation. General solvability of the equation has been proved ...