$L_{loc}^1$-convergence of Jacobians of Sobolev homeomorphisms via area formula

Zofia Grochulska

We prove that given a sequence of homeomorphisms $f_k:\Omega \to {\mathbb{R}}^n$ convergent in $W^{1,p}(\Omega ,{\mathbb{R}}^n)$, $p\ge 1$ for $n=2$ and $p>n-1$ for $n\ge 3$, to a homeomo…