February 15/16: Existence and uniqueness ¡­

February 15/16: Existence and uniqueness theory was developed for polyconvex integral functionals. Furthermore, minimization problems with integral constraints were analyzed, including proving existence of minimizers and deriving the corresponding Euler-Lagrange equation. The E-L equation took the form of a nonlinear eigenvalue problem with the eigenvalue being the Lagrange multiplier of the integral constraint. Next week's topics are minimization problems with pointwise one-sided constraints and pointwise constraints (the latter will be exemplified by the problem of harmonic maps into spheres and the incompressible Stokes' problem).