Distortion theorems for homeomorphic Sobolev mappings of integrable p-dilatations - AFANAS’EVA, Elena; GOLBERG, Anatoly; SALIMOV, Ruslan (Studia Universitatis Babeș-Bolyai Mathematica, 2022)
We study the distortion features of homeomorphisms of Sobolev class loc admitting integrability for p-outer dilatation. We show that such map- pings belong to W 1,n−1, are differentiable almost everywhere and possess absolute continuity in measure. In addition, such mappings are both ring and lower Q-homeomorphisms with appropriate measurable functions Q. This allows us to derive various distortion results like Lipschitz, H¨older, logarithmic H¨older conti- nuity, etc. We also establish a weak bounded variation property for such class of homeomorphisms. Mathematics Subject Classification (2010): 30C65, 26B35, 46E35. Received 19 January 2022; Accepted 18 March 2022.