Про неперервність розв'язків рівнянь Бельтрамі за Гельдером

V.  Ryazanov; R.  Salimov; E.  Sevost’yanov

doi:10.37863/umzh.v75i4.7464

V. Ryazanov Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, Slovyansk, Donetsk region; Cherkasy National University named after Bohdan Khmelnytskyi
R. Salimov Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv
E. Sevost’yanov Zhytomyr Ivan Franko State University; Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, Slovyansk, Donetsk region.

DOI: https://doi.org/10.37863/umzh.v75i4.7464

Keywords: Beltrami equations, Holder continuity

Abstract

UDC 517.5

We consider the problem of local behavior of solutions of the Beltrami equations in arbitrary domains. We have found sufficient conditions for the complex coefficient of the Beltrami equation guaranteeing the existence of its Hölder continuous solution in an arbitrary domain. These results can be used in the boundary-value problems for the Beltrami equation, as well as in the hydromechanics of strongly anisotropic and inhomogeneous media.

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On Hölder continuity of solutions of the Beltrami equations

Abstract

References