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.
VEN 10 ore 14, MER 15 ore 10, VEN 17 ore 14, MER 22 ore 10, VEN 24 ore 14
AULA 10, RM018