Sobolev mappings and moduli inequalities on Carnot groups

Abstract

In the article we study mappings of Carnot groups satisfy moduli inequalities. We prove that homeomorphisms satisfy the moduli inequalities ($Q$-homeomor\-phisms) with a locally integrable function $Q$ are Sobolev mappings. On this base in the frameworks of the weak inverse mapping theorem we prove that mappings inverse to Sobolev homeomorphisms of finite distortion of the class $W_{\nu ,\text{loc}}^1(\Omega ;{\Omega }^{\prime })$ belong to the Sobolev class $W_{1,\text{loc}}^1({\Omega }^{\prime };\Omega )$.

14 pages