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Homeomorphisms that induce monomorphisms of Sobolev spaces

Research paper by V. Gol’dshtein, L. Gurov, A. Romanov

Indexed on: 01 Oct '95Published on: 01 Oct '95Published in: Israel Journal of Mathematics



Abstract

LetG, G′ be domains in ℝn. We obtain a geometrical description of the class of all homeomorphisms ϕ:G→ G′ that induce bounded operators ϕ* from the seminormed Sobolev spaceLp1(G′) toLp1(G) by the rule ϕ*u =u o ϕ. Forp-Poincare domains the same classes of homeomorphisms induce bounded operators for classical Sobolev spacesWp1. These classes of homeomorphisms are natural generalizations of the class of quasiconformal homeomorphisms that correspond to the casep=n. We demonstrate some applications of our results for embedding theorems in domains with Hölder singularities.