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<p>We study the mappings distorting the moduli of the families of paths according to the Poletsky-type inequality. At the boundary points of a domain, we obtain estimates for the distortion of distances by these mappings under the condition that their characteristic either has a finite mean oscillation at every point or satisfies the Lehto-type integral conditions, while the mapped domain is Ahlfors regular and satisfies the Poincaré inequality. We analyze the cases of homeomorphisms and mappings with branching, as well as the domains with good boundaries and domains with prime ends.</p>

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On the Boundary Estimates for the Distortion of Mappings in Domains With Poincaré Inequalities

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Evgeny Sevost’yanov,
  • Mariya Baronova,
  • Oleksandr Dovhopiatyi,
  • Nataliya Ilkevych

摘要

We study the mappings distorting the moduli of the families of paths according to the Poletsky-type inequality. At the boundary points of a domain, we obtain estimates for the distortion of distances by these mappings under the condition that their characteristic either has a finite mean oscillation at every point or satisfies the Lehto-type integral conditions, while the mapped domain is Ahlfors regular and satisfies the Poincaré inequality. We analyze the cases of homeomorphisms and mappings with branching, as well as the domains with good boundaries and domains with prime ends.