Annales Academię Scientiarum Fennicę
Mathematica
Volumen 35, 2010, 285-289

ON REGULAR HOMEOMORPHISMS IN THE PLANE

Ruslan Salimov

National Academy of Sciences of Ukraine, Institute of Applied Mathematics and Mechanics
74 Roze Luxemburg str., 83114 Donetsk, Ukraine; salimov 'at' iamm.ac.donetsk.ua

Abstract. A regular homeomorphism of the Sobolev class W_loc^1,1 in the plane domain D is a ring Q-homeomorphism with Q(z) = K_\mu^T(z,z₀) where K_\mu^T(z,z₀) is the tangential dilatation of f at z₀ \in D.

2000 Mathematics Subject Classification: Primary 30C65; Secondary 30C75.

Key words: Ring Q-homeomorphisms, regular homeomorphisms, modulus, absolute continuity on lines, differentiability, Sobolev's classes.

Reference to this article: R. Salimov: On regular homeomorphisms in the plane. Ann. Acad. Sci. Fenn. Math. 35 (2010), 285-289.

Full document as PDF file

doi:10.5186/aasfm.2010.3517

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