Stefan Hollands

Jörg Lehnert

Inselstraße 22
04103 Leipzig


Lectures in the Winter Semester 2017/2018

Due to the rather broad spectrum of topics within the IMPRS, the curriculum consists of a core curriculum to be attended by all students and a variety of more specialized lectures and courses. The heart of our teaching program certainly is the Ringvorlesung. Each semester the Ringvorlesung focuses on one field and is usually delivered by three scientific members of the IMPRS who introduce three different approaches and visions within this field.

IMPRS Ringvorlesung "Partial Differential Equations"

General information

  • Time and location lecture: Thursday 09:00 - 11:00, MPI MiS E1 05
  • Lecturer: Benjamin Gess, Felix Otto, László Székelyhidi
  • Time and location exercises: Tuesday 13:30 - 15:00, MPI MiS G2 01
  • Tutor: Benjamin Fehrmann
  • Target audience: MSc students, PhD students, Postdocs
  • Content (Keywords):
    • Gess: shocks, entropy solutions, Lax-Oleinik formula, kinetic solutions
    • Székelyhidi:mean value property, maximum principle, unique continuation, Dirichlet principle
    • Otto: Lp-theory (Calderon-Zygmund theory), Cα-theory (Schauder theory)
  • Videos from all lectures: Every lecture will be recorded and can be viewed later. For more info, streaming and download see the media WWW page at the MPI MIS.
  • Prerequisites: Basic analysis (Lebesgue integration, Lebesgue spaces, Gauss’s theorem etc.), characteristics (Evans, Chapter 3.2)


  • Benjamin Gess: Scalar conservation laws (5 lectures, 12.10. - 09.11.)
  • László Székelyhidi: Basic properties of harmonic functions (5 lectures, 16.11. - 14.12.)
  • Felix Otto: Regularity theory for elliptic equations (04.01. - 01.02.)


  • Scalar conservation laws:
    Evans: Partial differential equations, Chapter 3.4
    Perthame: Kinetic formulation of conservation laws, Chapter 3
  • Basic properties of harmonic functions:
    Evans: Partial differential equations, Chapter 3.2
  • Regularity theory for elliptic equations:
    Krylov: Lectures on elliptic and parabolic equations in Hoelder spaces, Chapter 3
06.09.2023, 15:01