Variational problems of nonlinear elasticity theory in certain classes of mappings with finite distortion

A. O. Molchanova, S. K. Vodop'yanov

We study the problem of minimizing the functional $$I(\phi )=\underset{\Omega }{\int }W(x,D\phi )dx$$ on a new class of mappings. We relax summability conditions for admissible deformations to $φ…