Aperiodic fractional obstacle problems

Details Aperiodic fractional obstacle problems Aperiodic fractional obstacle problems

2009-09-28

arxiv.org/abs/0909.5042v1

Mathematics

Analysis of PDEs

Scientific paper

We determine the asymptotic behaviour of (bilateral) obstacle problems for fractional energies in rather general aperiodic settings via Gamma-convergence arguments. As further developments we consider obstacles with random sizes and shapes located on points of standard lattices, and the case of random homothetics obstacles centered on random Delone sets of points. Obstacle problems for non-local energies occur in several physical phenomenona, for which our results provide a description of the first order asympotitc behaviour.

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