

Regularity theory for nonlinear, degenerate partial differential equations
- Lecturer: Benjamin Gess
- Date: Monday 16:15 - 17:45
- Room: MPI MiS, A3 01
- Language: English
- Target audience: MSc students, PhD students, Postdocs
- Prerequisites: Basic PDE courses, functional analysis
Abstract:
In this lecture we will focus on the porous medium equation. The porous medium equation arises, for example, as a model for the flow of an ideal gas in a porous medium. The degenerate nature of the diffusivity of this PDE leads to interesting effects such as limited regularity of solutions, finite speed of propagation, open interfaces, waiting times etc. We will first recall several applications of the porous medium equation, consider special (self-similar) solutions and highlight particular properties of solutions to degenerate PDE. Then, we will focus on the question of (optimal) regularity of solutions to porous media equations, which relies on methods from harmonic analysis (Fourier multipliers, interpolation theory, Besov spaces) which will be recalled in the course of the lecture.
Regular Lectures (Summer 2018)
- Geometric and topological methods of data analysis
- Jürgen Jost
- Friday, 13:30 - 15:00, MPI MiS A3 01
- Regularity theory for nonlinear, degenerate partial differential equations
- Benjamin Gess
- Monday, 16:15 - 17:45, MPI MiS A3 01
- The signature of iterated integrals: algebra, analysis and machine learning
- Joscha Diehl
- Thursday, 09.00-10.30, A3 02
- Geometric Variational Problems
- Ulrich Menne
- Monday & Friday, 9:15 - 10:45, Augusteum, Room 314
- The Calderón Problem
- Angkana Rüland
- Thursday, 13:15-14:45, Augusteum, Room 314
- Introduction to the KPZ Equation
- Scott Smith
- Monday, 10:30 - 12:30, MPI MiS A3 01
- Low-rank tensor approximation
- André Uschmajew
- Thursday, 11:00 - 12:30, MPI MiS G3 10
- Data: crush course
- Ivan P. Yamshchikov
- Friday, 12.00-13.30, A3 02
- Stochastic homogenization
- Felix Otto
- Wednesday, 09:15 - 11:00, MPI MiS A3 01
- Reading seminar on “J-holomorphic curves”
- Enno Keßler and Ruijun Wu
- Wednesday, 13:00 - 14:30, MPI MiS A3 01
- IMPRS-Ringvorlesung: Introduction to Nonlinear Algebra
- Bernd Sturmfels and Mateusz Michałek
- Tuesday, 10:00 - 12:00, MPI MiS G3 10