Sobolev mappings and moduli inequalities on Carnot groups

摘要

We study the mappings that satisfy moduli inequalities on Carnot groups. We prove that the homeomorphisms satisfying the moduli inequalities (Q-homeomorphisms) with a locally integrable function Q are Sobolev mappings. On this base in the frameworks of the weak inverse mapping theorem, we prove that, on the Carnot groups G, the mappings inverse to Sobolev homeomorphisms of finite distortion of the class W_(υ,loc)~1(Ω; Ω') belong to the Sobolev class W_(1,loc)~1(Ω; Ω').