Minimization Problems Involving Policonvex Integrands

Dissertation Defense
Friday, April 24, 2015 - 13:30
1 hour (actually 50 minutes)
Skiles 249
School of Mathematics, Georgia Tech
This thesis is mainly concerned with problems in the areas of the Calculus of Variations and Partial Differential Equations (PDEs). The properties of the functional to minimize play an important role in the existence of minimizers of integral problems. We will introduce the important concepts of quasiconvexity and polyconvexity. Inspired by finite element methods from Numerical Analysis, we introduce a perturbed problem which has some surprising uniqueness properties.