Geodesic
Quantitative convergence of the “bulk” free boundary in an oscillatory obstacle problem
Farhan Abedin1 orcid ; William M. Feldman2 orcid
1Lafayette College, Easton, USA
2University of Utah, Salt Lake City, USA
Interfaces and free boundaries, Tome 26 (2024) no. 1, pp. 31-44

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DOI

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.
DOI : 10.4171/ifb/501
Classification : 35-XX
Mots-clés : obstacle problem, homogenization, free boundaries, large scale regularity

Farhan Abedin  1   ; William M. Feldman  2

1 Lafayette College, Easton, USA
2 University of Utah, Salt Lake City, USA 
Farhan Abedin; William M. Feldman. Quantitative convergence of the “bulk”  free boundary in an oscillatory obstacle problem. Interfaces and free boundaries, Tome 26 (2024) no. 1, pp. 31-44. doi: 10.4171/ifb/501
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     author = {Farhan Abedin and William M. Feldman},
     title = {Quantitative convergence of the {\textquotedblleft}bulk{\textquotedblright}  free boundary in an oscillatory obstacle problem},
     journal = {Interfaces and free boundaries},
     pages = {31--44},
     year = {2024},
     volume = {26},
     number = {1},
     doi = {10.4171/ifb/501},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/501/}
}
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