MTH 619: Convex Analysis and PDEs

The minimization of quadratic functions over closed convex subsets has classical applications to boundary-value problems for elliptic partial differential equations, variational inequalities and optimal control problems, penalty or augmented Lagrangian methods and mixed formulations. We shall develop these ideas and applications to boundary-value problems and algorithms for their approximation. These topics will be placed in the more general context of convex analysis, saddle points and Lagrange multipliers, primal and dual problems in Hilbert space. These concepts will be illustrated with examples from mechanics (internal or boundary obstacles, friction), fluid flow (Stokes or Bingham flow) and diffusion (heat conduction, porous media flow).
The choice of Topics covered and Examples developed will depend in part on preferences of the class.

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