Homogenization results for the generator of multiscale Langevin dynamics in weighted Sobolev spaces
Andrea Zanoni · IMA Journal of Applied Mathematics · 2023
Abstract We study the homogenization of the Poisson equation with a reaction term and of the eigenvalue problem associated to the generator of multiscale Langevin dynamics. Our analysis extends the theory of two-scale convergence to the case of weighted Sobolev spaces in unbounded domains. We provide convergence results for the solution of the multiscale problems above to their homogenized surrogate. A series of numerical examples corroborate our analysis.