Super regularity for Beltrami systems

2019/03/03 by Martin, Gaven J.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.01008

Abstract

We prove a surprising higher regularity for solutions to the nonlinear elliptic autonomous Beltrami equation in a planar domain Ω, f_\zbar = \cal A(f_z) \hskip15pt a.e. z∈ Ω, when \cal A is linear at ∞. Namely W^1,1_loc(Ω) solutions are W^2,2+ε_loc(Ω). Here ε>0 depends explicitly on the ellipticity bounds of \cal A. The condition ``is linear at ∞'' is necessary - the result is false for the equation f_\zbar = k|f_z|, for any 0

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