P. Bella (TU Dortmund)
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  This talk addresses regularity for elliptic equations under merely averaged
  ellipticity conditions and establishes sharp criteria ensuring local boundedness
  and Harnack inequalities. These results extend the classical De
  Giorgi–Nash–Moser theory and yield new applications to variational
  integrals with
(p, q)-growth. In the second part, the same regularity ideas are applied to the
random conductance model, leading–under optimal moment assumptions–to
  a quenched invariance principle and a local limit theorem. The results
  highlight a close connection between regularity theory and stochastic
  homogenization.