Calcolo delle variazioni e PDE
• Calculus of Variations
Variational problems in the space BV of functions of bounded variation.
Lower semicontinuity for integral (and supremal) functionals in BV.
Relaxation and integral representation of relaxed functionals in BV.
Lower semicontinuity for polyconvex integrals.
• Elliptic Equations
Dirichlet forms and degenerate elliptic equations.
Asymptotic problems for Dirichlet forms.
Elliptic nonlinear equations on unbounded domains.
• Conservation Laws
Applications of the chain rule formula in BV to the conservation laws.