Lecturer:
Course Type:
PhD Course
Academic Year:
2013-2014
Period:
November-January
Duration:
20 h
Description:
- Elements of convex analysis, polar and bipolar function and their properties, convex envelopes. Semiclassical theory, Euler-Lagrange equations and relation with elliptic PDE’s. Regularity of minimizers.
- Direct method, quasiconvexity, polyconvexity, rank-one convexity and their relations. Semicontinuity theorems for scalar and vectorial functionals; existence of minimizers.
- Relaxation theorems, representation of relaxed functionals; convex, quasiconvex, polyconvex and rank-one convex envelopes.
- Non semicontinuous problems. Hamilton-Jacobi equations, differential inclusions and applications to non convex problems.
Research Group: