Sobolev mappings and moduli inequalities on Carnot groups

Evgenii Sevost'yanov; Alexander Ukhlov

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arXiv · 2003.13437

Sobolev mappings and moduli inequalities on Carnot groups

Evgenii Sevost'yanov·Alexander Ukhlov

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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 $W^1_{\nu,\text{loc}}(\Omega;\Omega')$ belong to the Sobolev class $W^1_{1,\text{loc}}(\Omega';\Omega)$.

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Evgenii Sevost'yanov, Alexander Ukhlov. 2020-03-30. Sobolev mappings and moduli inequalities on Carnot groups. https://arxiv.org/abs/2003.13437

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