Tutorial by Andrej Cherkaev, May 16, 1:30 - 3:30 pm

1. Convexity, Convex envelope. Caratheodori theorem.


2. Oscillating solutions in one-dimensional variational problems.
   Identification of oscillating solutions and description of their limiting behavior.


3. Concentration and growth conditions.


4. Multivariable variational problems with a scalar minimizer.
   Oscillatory solutions and laminates.


5. Notion of quasiconvexity and quasiconvex envelope.


6. Upper and lower bounds for quasiconvex envelope. An example.