Annales Academię Scientiarum Fennicę
Mathematica
Volumen 33, 2008, 295-301

ACL AND DIFFERENTIABILITY OF Q-HOMEOMORPHISMS

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. It is established that a Q-homeomorphism in Rⁿ, n\geq 2, is absolute continuous on lines, furthermore, in W^1,1_loc and differentiable a.e. whenever Q\in L¹_loc.

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

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

Reference to this article: R. Salimov: ACL and differentiability of Q-homeomorphisms. Ann. Acad. Sci. Fenn. Math. 33 (2008), 295-301.

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