Mappings with finite distortion and arbitrary Jacobian sign

摘要

We consider some classes of mappings F: D → R~n which are ACLn and ||f'(x)||~n ≤ K · |J_f(x)| a.e. Such mappings generalize quasiregular mappings, but are not necessarily open, and the Jacobian not necessarily a constant sign and satisfy the K0(f) inequality. We also consider nonopen and nonsingular mappings F: D → R~n with bounded dilatation K_a and we show that such mappings satisfy a strong ACL condition, extending in this way some results from (Kallunki, 2002, Mappings of finite distortion: The metric definition. Ann. Acad. Sci. Fenn, Math., Diss.., 131, 1-33).