Sobolev regularity of quasiconformal mappings on domains

2015/07/15 by Prats, Martí
#30C62 #42B37 #46E35 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1507.04332

Abstract

Consider a Lipschitz domain Ω and a measurable function μ supported in Ω with ‖μ‖_L^∞<1. Then the derivatives of a quasiconformal solution of the Beltrami equation ∂ f =μ∂ f inherit the Sobolev regularity W^n,p(Ω) of the Beltrami coefficient μ as long as Ω is regular enough. The condition obtained is that the outward unit normal vector N of the boundary of the domain is in the trace space, that is, N∈ B^n-1/p_p,p(∂Ω).

Related

• Beltrami equations with coefficient in the Sobolev space W^1,p
• Quantitative Sobolev regularity of quasiregular maps
• Extremal properties of Sobolev's Beltrami coefficients and distortion of curvelinear functionals
• Beltrami equations in the plane and Sobolev regularity
• Quasiconformal maps with controlled Laplacian