Periodic homogenization of the principal eigenvalue of second-order elliptic operators
Analysis of PDEs
2022-05-11 v1
Abstract
In this paper we investigate homogenization results for the principal eigenvalue problem associated to -homogeneous, uniformly elliptic, second-order operators. Under rather general assumptions, we prove that the principal eigenpair associated to an oscillatory operator converges to the eigenpair associated to the effective one. This includes the case of fully nonlinear operators. Rates of convergence for the eigenvalues are provided for linear and nonlinear problems, under extra regularity/convexity assumptions. Finally, a linear rate of convergence (in terms of the oscillation parameter) of suitably normalized eigenfunctions is obtained for linear problems.
Keywords
Cite
@article{arxiv.2205.04963,
title = {Periodic homogenization of the principal eigenvalue of second-order elliptic operators},
author = {Gonzalo Dávila and Andrei Rodríguez-Paredes and Erwin Topp},
journal= {arXiv preprint arXiv:2205.04963},
year = {2022}
}