• Lecturer: Felix Otto
• Date: Tuesday 09:15 - 11:00
• Room: MPI MiS, A 01
• Language: English
• Target audience: MSc students, PhD students, Postdocs
• Content (Keywords): linear elliptic differential equations with random coefficient fields, elliptic regularity theory
• Prerequisites: Some knowledge in elliptic PDE is helpful, practically no knowledge in Probability theory

Abstract

We are interested in linear elliptic differential equations (including the case of systems) with random coefficient fields. Provided the underlying probability measure on the space of coefficient fields is shift invariant and ergodic, the solution operator acts on large scales like the solution operator of an elliptic equation with deterministic and spatially homogeneous coefficients; a phenomenon called homogenization. We are interested in quantitative aspects of this phenomenon. It turns out that this is intimately linked to elliptic regularity theory; in fact, the above type of randomness generates a large-scale regularity theory as for instance encoded in Liouville properties.