--- res: bibo_abstract: - We construct planar bi-Sobolev mappings whose local volume distortion is bounded from below by a given function f∈Lp with p>1. More precisely, for any 1<q<(p+1)/2 we construct W1,q-bi-Sobolev maps with identity boundary conditions; for f∈L∞, we provide bi-Lipschitz maps. The basic building block of our construction are bi-Lipschitz maps which stretch a given compact subset of the unit square by a given factor while preserving the boundary. The construction of these stretching maps relies on a slight strengthening of the celebrated covering result of Alberti, Csörnyei, and Preiss for measurable planar sets in the case of compact sets. We apply our result to a model functional in nonlinear elasticity, the integrand of which features fast blowup as the Jacobian determinant of the deformation becomes small. For such functionals, the derivation of the equilibrium equations for minimizers requires an additional regularization of test functions, which our maps provide.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Julian L foaf_name: Fischer, Julian L foaf_surname: Fischer foaf_workInfoHomepage: http://www.librecat.org/personId=2C12A0B0-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-0479-558X - foaf_Person: foaf_givenName: Olivier foaf_name: Kneuss, Olivier foaf_surname: Kneuss bibo_doi: 10.1016/j.jde.2018.07.045 bibo_issue: '1' bibo_volume: 266 dct_date: 2019^xs_gYear dct_identifier: - UT:000449108500010 dct_language: eng dct_publisher: Elsevier@ dct_title: Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with L p data and applications to nonlinear elasticity@ ...