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 PDEs and systems.
  • Semigroups 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.