Jiwoong Jang
Published 2024-01-15Version 1
Proving homogenization has been a subtle issue for geometric equations due to the discontinuity when the gradient vanishes. A sufficient condition for periodic homogenization using perturbed correctors is suggested in the literature [3] to overcome this difficulty. However, some noncoercive equations do not satisfy this condition. In this note, we prove homogenization of geometric equations without using perturbed correctors, and therefore we conclude homogenization for the noncoercive equations. Also, we provide a rate of periodic homogenization of coercive geometric equations by utilizing the fact that they remain coercive under perturbation. We also present an example that homogenizes with a rate $\Omega(\varepsilon|\log \varepsilon|)$.
Lectures on Periodic Homogenization of Elliptic Systems
Regularity of Homogenized Boundary Data in Periodic Homogenization of Elliptic Systems
On optimal rate of convergence in periodic homogenization of forced mean curvature flow of graphs in the laminar setting
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