No abstract

We show that a sufficient condition for the weak limit of a sequence of W 1 q -homeomorphisms with finite distortion to be almost everywhere injective for q ≥ n − 1, can be stated by means of composition operators. Applying this result, we study nonlinear elasticity problems with respect to these new classes of mappings. Furthermore, we impose loose growth conditions on the stored-energy function for the class of W 1 n -homeomorphisms with finite distortion and integrable inner as well as outer distortion coefficients.

No abstract

We present a simple proof of the continuity, in the sense distributions, of the minors of the differential matrices of mappings belonging to grand Sobolev spaces. Such function spaces were introduced in connection with a problem on minimal integrability of the Jacobian and are useful in certain aspects of geometric function theory and partial differential equations.