On the local properties of solutions of the nonlinear Beltrami equation

Abstract

A power estimate of the area of the image of a disk for regular homeomorphisms possessing the Luzin N-property is obtained in terms of the p-angular dilation for p > 2. The result generalizes the known estimate by M.A. Lavrent’ev. A number of theorems on the asymptotic behavior of regular homeomorphic solutions of the nonlinear Beltrami equation are proved, and an extreme analog of the Ikoma–Schwartz lemma is formulated.

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Correspondence to Ruslan R. Salimov.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 17, No. 1, pp. 77–95 January–March, 2020.

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Salimov, R.R., Stefanchuk, M.V. On the local properties of solutions of the nonlinear Beltrami equation. J Math Sci 248, 203–216 (2020). https://doi.org/10.1007/s10958-020-04870-6

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Keywords

  • Beltrami equation
  • regular homeomorphism
  • N-property
  • p-angular dilation
  • regular homeomorphic solution of the equation