Bi-Sobolev mappings and elliptic equations in the plane

Abstract

Suppose that $f=(u,v)$ is a homeomorphism in the plane of the Sobolev class $W^{1,1}_{\loc}$ such that its inverse is of the same Sobolev class. We prove that $u$ and $v$ have the same set of critical points.

We study similar question in higher dimension.

Keywords

• Bi-Sobolev
• mappings
• elliptic
• equations
• plane