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On the compactness of classes of the solutions of the Dirichlet problem


Some theorems concerning the compact classes of homeomorphisms with hydrodynamic normalization, which are solutions of the Beltrami equation and the characteristics of which are compactly supported and satisfy certain constraints of the theoretical-set type, have been proved. As a consequence, we obtained results on the compact classes of solutions of the corresponding Dirichlet problems considered in a certain Jordan domain.

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Corresponding author

Correspondence to Oleksandr P. Dovhopiatyi.

Additional information

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 18, No. 3, pp. 319–337, July–September, 2021.

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Dovhopiatyi, O.P., Sevost’yanov, E.A. On the compactness of classes of the solutions of the Dirichlet problem. J Math Sci 259, 23–36 (2021).

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  • Quasiconformal analysis
  • convergence theorems
  • compactness theorems
  • Beltrami equation