Toward the theory of the Sobolev classes with critical exponent

Abstract

It is established that an arbitrary homeomorphism f in the Sobolev class W1,n−1loc with the outer dilatation K0(x,f)∈Ln−1loc is the socalled lower Q - homeomorphism with Q=K0(x,f) and the ring Q* homeomorphism with Q∗=Kn−10(x,f). These results make it possible to research the local and boundary behaviors of the mappings W1,n−1loc

Keywords

• critical exponent
• outer and inner dilatations
• lower and ring Q homeomorphisms
• outer and inner dilatations