Abstract
In this paper we investigate homogenization results for the principal eigenvalue problem associated to 1-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.
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Acknowledgements
We wish to express our gratitude to the anonymous referee for the thorough review of a previous version of this article. Their remarks and revisions allowed us to improve our results to a greater generality and also make the presentation clearer.
Funding
A. R.-P. was partially supported by Fondecyt Grant Postdoctorado Nacional No. 3190858. G. D. was partially supported by Fondecyt Grant No. 1190209. E. T. was partially supported by Fondecyt Grant No. 1201897.
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Dávila, G., Rodríguez-Paredes, A. & Topp, E. Periodic Homogenization of the Principal Eigenvalue of Second-Order Elliptic Operators. Appl Math Optim 88, 5 (2023). https://doi.org/10.1007/s00245-023-09979-z
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DOI: https://doi.org/10.1007/s00245-023-09979-z