MA8105 Nonlinear PDEs and Sobolev spaces · Spring 2021

About the course

  • The course covers mathematical methods and structures that are fundamental for the study of partial differential equations (PDEs), variational calculus, numerical methods etc.
  • The main focus is on analytical tools: Functional analysis, \(L^p\) and Sobolov spaces, compactness, modes of convergence, distributions, error estimates.
  • We cover some applications to linear and nonlinear PDEs.


When physical lectures are permitted:

  • Thursdays 14:15–16:00 in F3
  • Fridays 08:15–10:00 in F3

Otherwise, virtual lectures are held at the same times.

No physical lectures in the first week of the term (week 2). Lectures will be by zoom. We will post the link on Blackboard, and email it to those who cannot get it there.

Target audience

  • Interested students at Master or PhD level.
  • The course should be suitable for good 4th year students in the industrial mathematics program.
  • It can be taken as a regular course or a fordypningsemne.
  • Very relevant for students specialising in PDEs, optimisation, analysis, numerical analysis, or probability.


  • Elementary functional analysis, equivalent to TMA4145 Linear Methods.
  • Some real analysis (Lebesgue integration theory).
  • It is advantageous, but not necessary, to have some background in partial differential equations.

Sergei Lvovich Sobolev (Серге́й Льво́вич Со́болев, 1908–1989) · Wikipedia · MacTutor biography

Photo (© 1970) Konrad Jacobs

2021-01-29, Harald Hanche-Olsen