VAPS61:"Periodic homogenization of geometric equations without perturbed correctors"

Speaker: Jiwoong Jang, University of Maryland
Abstract: Proving homogenization is a subtle issue for geometric equations due to the discontinuity when the gradient vanishes. To conclude homogenization, the work of Caffarelli-Monneau provides a sufficient condition, namely that perturbed correctors exist. However, some noncoercive equations recently studied do not satisfy this condition. In this talk, we present the homogenization result of geometric equations without using perturbed correctors. For coercive equations, a quantitative result is derived by the fact that they remain coercive under perturbation. We present an example that homogenizes with a rate slower than O(\varepilon) in the last part.