Hydrodynamic normalization conditions in the theory of degenerate Beltrami equations
DOI:
https://doi.org/10.15407/dopovidi2023.02.010Keywords:
BMO, bounded mean oscillation, FMO, finite mean oscillation, degenerate Beltrami equations, hydrodynamic normalizationAbstract
We study the existence of normalized homeomorphic solutions for the degenerate Beltrami equation fz = μ(z )f in the whole complex plane C , assuming that its measurable coefficient μ(z ), | μ(z ) |<1 a. e., has compact support and the degeneration of the equation is controlled by the tangential dilatation quotient KT μ (z , z0) . We show that if KT μ (z , z0) has bounded or finite mean oscillation dominants, or satisfies the Lehto type integral divergence condition, then the Beltrami equation admits a regular homeomorphic W1,1loc solution f with the hydrodynamic normalization at infinity. We also give integral criteria of Calderon-Zygmund or Orlicz types for the existence of the normalized solutions in terms of KT μ (z , z0) and the maximal dilatation Kμ (z ) .
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