The relaxation of non-quasiconvex variational integrals
For non-quasiconvex variational integrals of the form \(E(u)= \int_{\Omega} w(\nabla u(x)) dx\), where \(u\in W^{1,p}(\Omega)\), \(p\geq 2\), it is shown that a multi-level infinite-dimensional variant of the steepest descent algorithm in connection with wiggly energies yields minimizing sequences that converge to a global minimum. The given method is applied to the minimization of variational problems associated with martensitic branching.
scientific article; zbMATH DE number 1310782