101.694 Selected topics in elliptic regularity theory

2023W, VO, 2.0h, 3.0EC


  • Semester hours: 2.0
  • Credits: 3.0
  • 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

Mode of examination




Course dates

Mon12:00 - 13:0002.10.2023Sem.R. DA grün 06B Vorbesprechung

Examination modalities

oral exam

Course registration

Not necessary


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No lecture notes are available.

Previous knowledge

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



if required in English