2021/12/15 by V. Gutlyanskii, V. Ryazanov, Gutlyanskii, V. +5
Engineering · Mathematics · #30C65 #30H35 #35J70 Secondary 35Q35 #76B03 #Aerospace Engineering and Control Systems #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Primary 30C62
paper · pdf · doi:10.48550/arxiv.2112.08937
openalex publication_date 2021/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
First of all, we prove that the BMO condition by John-Nirenberg leads in the natural way to the asymptotic homogeneity at the origin of regular homeomorphic solutions of the degenerate Beltrami equations. Then on this basis we establish a series of criteria for the existence of regular homeomorphic solutions of the degenerate Beltrami equations in the whole complex plane with asymptotic homogeneity at infinity. These results can be applied to the fluid mechanics in strictly anisotropic and inhomogeneous media because the Beltrami equation is a complex form of the main equation of hydromechanics.