On quasilinear Beltrami-type equations with degeneration |
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Authors: | E. A. Sevost’yanov |
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Affiliation: | 1. Institute for Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk, Russia
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Abstract: | We consider the solvability problem for the equation $f_{bar z} $ = v(z, f(z))f z , where the function v(z,w) of two variables may be close to unity. Such equations are called quasilinear Beltrami-type equations with ellipticity degeneration. We prove that, under some rather general conditions on v(z,w), the above equation has a regular homeomorphic solution in the Sobolev classW loc 1,1 . Moreover, such solutions f satisfy the inclusion f ?1 ∈ W loc 1,2 . |
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