Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-70-12-K-7

Sobolev Spaces (4V+2U, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 9.0 CP 186 h
4 V Lecture 56 h
2 U Exercise class (in small groups) 28 h
(4V+2U) 9.0 CP 84 h 186 h

Basedata

SWS 4V+2U
CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-SPAS] Analysis and Stochastics
Additional informations
Livecycle-State [NORM] Active

Contents

  • extension of integration theory (convergence theorems, Lp-spaces, partial integration),
  • construction of Sobolev spaces,
  • analysis in Sobolev spaces (convolution, Dirac sequences, partition of unity, dense sets of functions),
  • applications to partial differential equations (Poincaré inequality, fundamental lemma of calculus of variations, weak formulation of boundary problems),
  • Sobolev embedding theorems and trace operator,
  • test function and distribution spaces,
  • analysis in distributions spaces (Fourier transform, differentiation, convolution),
  • dual spaces of Sobolev spaces,
  • fractional Sobolev spaces.

Literature

  • H.-W. Alt: Lineare Funktionalanalysis,
  • M. Dobrowolski: Angewandte Funktionalanalysis,
  • M. Reed, B. Simon: Functional Analysis I.

Materials

Further literature will be announced in the lecture; Exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

References to Course [MAT-70-12-K-7]

Module Name Context
[MAT-70-12-M-7] Sobolev Spaces P: Obligatory 4V+2U, 9.0 LP