Diffeomorphic Approximation of continuous almost everywhere injective Sobolev deformations in the plane

Abstrakt

In this note we prove that given a continuous Sobolev $W^{1,p}$ deformation $f$, with $1 < p < \infty$, from a planar domain to $\er^2$ which is injective almost everywhere, we can find a sequence $f_k$ of diffeomorphisms with $f_k - f \in W^{1,p}_0$ such that $f_k \to f$ uniformly and in the Sobolev norm.

Klíčová slova

• Sobolev space
• Approximation