Quantitative convergence of the "bulk'' free boundary in an oscillatory obstacle problem
Analysis of PDEs
2022-08-10 v1
Abstract
We consider an oscillatory obstacle problem where the coincidence set and free boundary are also highly oscillatory. We establish a rate of convergence for a regularized notion of free boundary to the free boundary of a corresponding classical obstacle problem, assuming the latter is regular. The convergence rate is linear in the minimal length scale determined by the fine properties of a corrector function.
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Cite
@article{arxiv.2208.04923,
title = {Quantitative convergence of the "bulk'' free boundary in an oscillatory obstacle problem},
author = {Farhan Abedin and William M Feldman},
journal= {arXiv preprint arXiv:2208.04923},
year = {2022}
}
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10 pages