Quantitative convergence of the "bulk'' free boundary in an oscillatory obstacle problem

Farhan Abedin; William M Feldman

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arXiv · 2208.04923

Quantitative convergence of the "bulk'' free boundary in an oscillatory obstacle problem

Farhan Abedin·William M Feldman

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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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Farhan Abedin, William M Feldman. 2022-08-09. Quantitative convergence of the "bulk'' free boundary in an oscillatory obstacle problem. https://arxiv.org/abs/2208.04923

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