Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-70-12A-K-7

Introduction to the Theory of Sobolev Spaces (2V+1U, 4.5 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 4.5 CP 93 h
2 V Lecture 28 h
1 U Exercise class (in small groups) 14 h
(2V+1U) 4.5 CP 42 h 93 h

Basedata

SWS 2V+1U
CP, Effort 4.5 CP = 135 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.

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-70-12A-K-7]

Module Name Context
[MAT-70-12A-M-7] Introduction to the Theory of Sobolev Spaces P: Obligatory 2V+1U, 4.5 LP