The linear Beltrami equation on the Riemann sphere is studied under assumption that its measurable complex-valued coefficient μ(z) has a compact support in ℂ and ‖μ‖∞ = 1 Sufficient conditions for existence of regular homeomorphic $$ {W}_{\mathrm{loc}}^{1,1} solutions to with hydrodynamic normalization at infinity are given, particular, provided either dilatation Kμ boundedmean- oscillation maj...

Abstract. An effective algorithm is presented for solving the Beltrami equation ∂f = μ ∂f in a planar disk. The algorithm involves no evaluation of singular integrals. The strategy, working in concentric rings, is to construct a piecewise linear μ-conformal mapping and then correct the image using a known algorithm for conformal mappings. Numerical examples are provided and the computational co...

We continue to study regular homeomorphic solutions the nonlinear Beltrami equation introduced in [24]. Estimates of Schwarz Lemma type have been obtained using length-area method.

The Beltrami framework for image processing and analysis introduces a non-linear parabolic problem, called in this context the Beltrami flow. We study in the framework for functions of bounded variation, the well-posedness of the Beltrami flow in the one-dimensional case. We prove existence and uniqueness of the weak solution using lower semi-continuity results for convex functions of measures....

An essentially unique homeomorphic solution to the Beltrami equation with measurable coefficients was found in 1930s by Morrey. The most well-known proof from 1960s uses theory of Calderón–Zygmund and singular integral operators $$L^p(\mathbb {C})$$ . We will present an alternative method solve using Hodge star operator standard elliptic PDE theory. also discuss a different prove regularity sol...

We study the dispersive properties of the wave equation associated with the shifted Laplace–Beltrami operator on real hyperbolic spaces and deduce new Strichartz estimates for a large family of admissible pairs. As an application, we obtain local well–posedness results for the nonlinear wave equation.