On the uniqueness of solutions of the Beltrami equation with a given real part on a boundary

Previously (2019), we established one result on the admissible rate of tending to zero of solutions of an equation of the form Δ𝑢 + 𝑐(𝑥)𝑢 = 0 at the ends of Riemannian manifolds with a metric of a special form. In this paper we show that in the two-dimensional case this result can be useful in solving problems of a slightly different type. Namely, for problems in the theory of functions of a complex variable. We have established a special version of the uniqueness theorem for the Beltrami equation = μ(𝑧)𝑤𝑧. Let us present this result. It is known that if ess sup𝐷′ |μ(𝑧)|