The Relaxation of Non-Quasiconvex Variational Integrals 1997


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    • Author:  by Petr Kloucek  Petr Kloucek  

    • Abstract:  We show that the Steepest Descent Algorithm in connection with wiggly energies yields minimizing sequences that converge to a global minimum of the associated non-quasiconvex variational integrals. We introduce a multi-level infinite dimensional variant of the Steepest Descent Algorithm designed to compute complex microstructures by forming non-smooth minimizers from the smooth initial guess. We apply this multilevel method to the minimization of the variational problems associated with martensitic branching. Keywords Quasiconvexity, nonconvex minimization, microstructures, steepest descent, wiggly energy, multi-level minimization methods, martensite, martensitic branching. 1991 Mathematical Subject Classification 35B27, 35E10, 49J45, 65C20, 65D15, 65K10 1 Introduction A continuum description of materials with fine structure often leads to minimization and dynamic problems that are extremely complex. In many cases, the reason is that the scale associated with the crystallographic (f...

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