Partial Differential Equations


A crash course on Sobolev spaces. Second order linear elliptic equations (existence of weak solutions; regularity in the interior and up to the boundary; maximum principles; Harnack inequality; De Giorgi-Nash-Moser theory). Second order linear parabolic equations (existence via Galerkin method; regularity theory and maximum principles). The Calculus of Variations (Euler-Lagrange equation; existence of minimizers; regularity; unilateral constraints: variational inequalities and free boundary problems). Nonvariational techniques (monotonicity and fixed point methods). Degenerate and singular PDEs (the p-Laplace equation; intrinsic scaling; the infinity Laplacian).

View Course Page

Research and Events


  • There is no information available on this topic.
More Events

Defended Theses

  • Some aspects of descent theory and applications
      Rui Rodrigues de Abreu Fernandes Prezado (January 2024)
      Maria Manuel Clementino
      Fernando Lucatelli Nunes
  • Comparability between different systems: star-shaped and convex transform orders
      Beatriz Ferreira Santos (December 2023)
      Paulo Eduardo Oliveira
      Idir Arab
  • On Lax Idempotent Monads in Topology
      Carlos Miguel Alves Fitas (December 2023)
      Maria Manuel Clementino
More Theses