Research Topics

• Coercive and noncoercive elliptic equations with discontinuous coefficients in unbounded domains.

• Elliptic equations with discontinuous coefficients in weighted spaces on bounded and unbounded domains.

• Exact controllability of hyperbolic problems in domains with imperfect interface.

• Homogenization of stationary and evolutionary boundary value problems in perforated and two-component domains.

• Non-standard Sobolev inequalities.

• Optimal design problems involving bulk and surface energies.

• Regularity of Elliptic PDE’s and Systems.

• Semigroup and spectral theory for evolution equations with applications to second and higher order elliptic operators with unbounded and singular coefficients: Maximal regularity, kernel estimates and asymptotic behaviour of solutions to parabolic problems.

• Symmetrization and Isoperimetric Inequalities.