Please be advised the lockingsystemintegration my not be available due to system maintenance. Please accept our apologies for any inconvenience.

# 101.A13 AKANA AKNUM Selected topics in elliptic regularity theory This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2023W

2023W, VO, 3.0h, 4.5EC

## Properties

• Semester hours: 3.0
• Credits: 4.5
• Type: VO Lecture
• Format: Presence

## Learning outcomes

After successful completion of the course, students are able to formulate and prove regularity results for solutions of elliptic partial differential equations. They have understood the foundations of the proofs.

## Subject of course

We discuss selected topic in the regularity theory of elliptic PDEs. Topics include

1) shift theorems in scales of Sobolev spaces

2) regularity theory of elliptic problems in polygons (the techniques of Kondratiev, Grisvard)

3) Morrey and Campanato spaces

4) Holder continuity of solutions of scalar elliptic problems (Theorem of De Giorgi)

The course will be based on (selected chapters) of the books

a) Gilbarg-Trudinger, elliptic partial differential equations of second order

b) Giaquinta-Martinazzi, an introduction to the regularity theory for elliptic systems, harmonic maps and minimal graphs

c) Jost, partial differential equations

## Teaching methods

classical lectures at the black board

Oral

## Course dates

DayTimeDateLocationDescription
Tue12:00 - 14:0003.10.2023 - 23.01.2024Sem.R. DA grün 06B VO elliptic regularity theory
Fri10:00 - 12:0006.10.2023 - 19.01.2024 DA04G10VO elliptic regularity theory
AKANA AKNUM Selected topics in elliptic regularity theory - Single appointments
DayDateTimeLocationDescription
Tue03.10.202312:00 - 14:00Sem.R. DA grün 06B VO elliptic regularity theory
Fri06.10.202310:00 - 12:00 DA04G10VO elliptic regularity theory
Tue10.10.202312:00 - 14:00Sem.R. DA grün 06B VO elliptic regularity theory
Fri13.10.202310:00 - 12:00 DA04G10VO elliptic regularity theory
Tue17.10.202312:00 - 14:00Sem.R. DA grün 06B VO elliptic regularity theory
Fri20.10.202310:00 - 12:00 DA04G10VO elliptic regularity theory
Tue24.10.202312:00 - 14:00Sem.R. DA grün 06B VO elliptic regularity theory
Fri27.10.202310:00 - 12:00 DA04G10VO elliptic regularity theory
Tue31.10.202312:00 - 14:00Sem.R. DA grün 06B VO elliptic regularity theory
Fri03.11.202310:00 - 12:00 DA04G10VO elliptic regularity theory
Tue07.11.202312:00 - 14:00Sem.R. DA grün 06B VO elliptic regularity theory
Fri10.11.202310:00 - 12:00 DA04G10VO elliptic regularity theory
Tue14.11.202312:00 - 14:00Sem.R. DA grün 06B VO elliptic regularity theory
Fri17.11.202310:00 - 12:00 DA04G10VO elliptic regularity theory
Tue21.11.202312:00 - 14:00Sem.R. DA grün 06B VO elliptic regularity theory
Fri24.11.202310:00 - 12:00 DA04G10VO elliptic regularity theory
Tue28.11.202312:00 - 14:00Sem.R. DA grün 06B VO elliptic regularity theory
Fri01.12.202310:00 - 12:00 DA04G10VO elliptic regularity theory
Tue05.12.202312:00 - 14:00Sem.R. DA grün 06B VO elliptic regularity theory
Tue12.12.202312:00 - 14:00Sem.R. DA grün 06B VO elliptic regularity theory

oral exam

Not necessary

## Curricula

Study CodeObligationSemesterPrecon.Info
860 GW Optional Courses - Technical Mathematics Not specified

## Literature

No lecture notes are available.

## Previous knowledge

good knowledge of real analysis, basic knowledge of PDEs such as Lax-Milgram Lemma

## Language

if required in English