Sobolev Mappings and Moduli Inequalities on Carnot Groups

Abstract

Abstract. 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 $$ {W}_{v,\mathrm{loc}}^1\left(\Omega; {\Omega}^{\prime}\right) $$ belong to the Sobolev class $$ {W}_{1,\mathrm{loc}}^1\left({\Omega}^{\prime };\Omega \right) $$ .