====== MA8105 Nonlinear PDEs and Sobolev spaces · Spring 2021 ======


===== About the course =====
  * Lecturers are [[https://folk.ntnu.no/hanche/|Harald Hanche-Olsen]] and [[https://folk.ntnu.no/holden/|Helge Holden]]
  * 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.

===== Lectures =====

When physical lectures are permitted:
  * Thursdays 14:15–16:00 in [[https://link.mazemap.com/TdAgc64K|F3]]
  * Fridays 08:15–10:00 in [[https://link.mazemap.com/TdAgc64K|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.

===== Prerequisites =====
  * Elementary functional analysis, equivalent to [[https://wiki.math.ntnu.no/tma4145/2016h/start|TMA4145 Linear Methods]].
  * Some real analysis (Lebesgue integration theory). 
  * It is advantageous, but not necessary, to have some background in partial differential equations.

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{{:ma8105:2021v:sobolev_s_l.jpeg?nolink |}}

Sergei Lvovich Sobolev (Серге́й Льво́вич Со́болев, 1908–1989)
· [[https://en.wikipedia.org/wiki/Sergei_Sobolev|Wikipedia]]
· [[https://mathshistory.st-andrews.ac.uk/Biographies/Sobolev/|MacTutor biography]]

Photo (© 1970) Konrad Jacobs