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).

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Research and Events


  • PhD Defense
    Fernando Lucatelli Nunes - Pseudomonads and Descent
    10:00 - Sala dos Capelos, Univ. Coimbra
    January 24, 2018
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Defended Theses

  • Descent theory of (T,V)-categories: global-descent and étale-descent
      Pier Giorgio Basile (September 2017)
      Maria Manuel Clementino
  • Representations of generalized quivers
      Artur Duarte Ferreira de Araújo (June 2017)
      Peter Gothen
  • On semisimple Hopf actions
      Deividi Ricardo Pansera (June 2017)
      Christian Edgar Lomp
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