We consider a class of homeomorphisms of the Sobolev space whose Jacobian may vanish on a set of positive measure but cannot be zero a.e. in . This class is defined by the bi-Sobolev condition
and reveals useful also in the theory of changes of variables for Sobolev functions.
Cite this article
Carlo Sbordone, Roberta Schiattarella, Critical points for Sobolev homeomorphisms. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 22 (2011), no. 2, pp. 207–222DOI 10.4171/RLM/596