On Beltrami equations and Hölder regularity
نویسنده
چکیده
We estimate the Hölder exponent α of solutions to the Beltrami equation ∂f = μ∂f , where the Beltrami coefficient satisfies ‖μ‖∞ < 1. Our estimate improves the classical estimate α ≥ ‖Kμ‖ , where Kμ = (1 + |μ|)/(1 − |μ|), and it is sharp, in the sense that it is actually attained in a class of mappings which generalize the radial stretchings. Some other properties of such mappings are also provided.
منابع مشابه
On Planar Beltrami Equations and Hölder Regularity
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.
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