MINICORSO -Felix Otto (MPI-MIS, Leipzig): Stochastic homogenization and large-scale regularity

Room 10, RM018: 10/02/2023 14:00-16:00, 15/02/2023 10:00-12:00, 17/02/2023 14:00-16:00, 22/02/2023 10:00-12:00, 24/02/2023 14:00-16:00

In this mini-course, I will introduce the concept of large-scale
regularity in case of a linear elliptic equation (or system) with
heterogeneous coefficients. It is based on a smallness (on average) of the
potentials of the harmonic coordinates, and proceeds via an intrinsic
Campanato iteration. I will then apply this to the case of a random
heterogeneous coefficient field, sampled from a stationary and ergodic
ensemble. I will try to be self-contained and closely follow Theorem 1 and
Lemma 1 in Gloria, Neukamm, and Otto ``A regularity theory for random
elliptic operators'', Milan J Math 2020.

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