Homogenisation of Nonlinear Dirichlet Problems in Randomly Perforated Domains

Explore the convergence of integral functionals with q-growth in randomly perforated domains through this 45-minute lecture by Caterina Zeppieri at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the study of n-dimensional bounded domains perforated by randomly distributed spherical holes with varying radii and centers. Discover how, in the small-perforations limit, an averaged nonlinear analogue of the capacitary term emerges, similar to the Cioranescu and Murat findings in the linear deterministic periodic case. Learn about the minimal assumptions required for finite expectation of nonlinear q-capacity in spherical holes, and understand why clustering holes do not impact the homogenisation procedure. This talk, part of the "New perspective on Shape and Topology Optimization" workshop, offers valuable insights into advanced mathematical concepts in domain perforation and functional analysis.