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Sobolev Mappings and Moduli Inequalities on Carnot Groups

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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 \( {W}_{1,\mathrm{loc}}^1\left({\Omega}^{\prime };\Omega \right) \).

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Authors and Affiliations

  1. I. Franko Zhytomyr State University, Zhytomyr, Ukraine

    Evgenii A. Sevost’yanov

  2. Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slavyansk, Ukraine

    Evgenii A. Sevost’yanov

  3. Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel

    Alexander Ukhlov

Authors
  1. Evgenii A. Sevost’yanov
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  2. Alexander Ukhlov
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Correspondence to Evgenii A. Sevost’yanov or Alexander Ukhlov.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 17, No. 2, pp. 215–233 April–June, 2020.

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Sevost’yanov, E.A., Ukhlov, A. Sobolev Mappings and Moduli Inequalities on Carnot Groups. J Math Sci 249, 754–768 (2020). https://doi.org/10.1007/s10958-020-04971-2

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