Weak regularity of the inverse under minimal assumptions

Abstract

Let ΩSUBSET OFR3 be a domain and let fELEMENT OFBVloc(Ω,R3) be a homeomorphism such that its distributional adjugate is a finite Radon measure. We show that its inverse has bounded variation f-1ELEMENT OFBVloc.

The condition that the distributional adjugate is finite measure is not only sufficient but also necessary for the weak regularity of the inverse.

Keywords

• Weak
• regularity
• inverse
• minimal
• assumptions