On planar Beltrami equations and Hoelder regularity

2006/12/15 by Ricciardi, Tonia
#30C62 #35J25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0612438

Abstract

We provide estimates for the Hölder exponent of solutions to the Beltrami equation \dbar f=μ\de f+ν\de f, where the Beltrami coefficients μ,ν satisfy ‖|μ|+|ν|‖_∞<1 and \Im(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, and we discuss the main properties of such mappings.

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