Aperiodic fractional obstacle problems
arXiv:0909.5042
Abstract
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.
References in corpus (3)
- Regularity theory for fully nonlinear integro-differential equations
- Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian
- An Exactly Solvable Phase-Field Theory of Dislocation Dynamics, Strain Hardening and Hysteresis in Ductile Single Crystals