Geodesic
Almost minimizers for the thin obstacle problem with variable coefficients
Seongmin Jeon1 orcid ; Arshak Petrosyan2 orcid ; Mariana Smit Vega Garcia3 orcid
1KTH Royal Institute of Technology, Stockholm, Sweden
2Purdue University, West Lafayette, USA
3Western Washington University, Bellingham, USA
Interfaces and free boundaries, Tome 26 (2024) no. 3, pp. 321-380

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DOI

We study almost minimizers for the thin obstacle problem with variable Hölder continuous coefficients and zero thin obstacle, and establish their C1,β regularity on the either side of the thin space. Under an additional assumption of quasisymmetry, we establish the optimal growth of almost minimizers as well as the regularity of the regular set and a structural theorem on the singular set. The proofs are based on the generalization of Weiss- and Almgren-type monotonicity formulas for almost minimizers established earlier in the case of constant coefficients.
DOI : 10.4171/ifb/507
Classification : 49N60, 35R35
Mots-clés : almost minimizers, thin obstacle problem, Signorini problem, Weiss-type monotonicity formula, Almgren’s frequency formula, regular set, singular set

Seongmin Jeon  1   ; Arshak Petrosyan  2   ; Mariana Smit Vega Garcia  3

1 KTH Royal Institute of Technology, Stockholm, Sweden
2 Purdue University, West Lafayette, USA
3 Western Washington University, Bellingham, USA 
Seongmin Jeon; Arshak Petrosyan; Mariana Smit Vega Garcia. Almost minimizers for the thin obstacle problem with variable coefficients. Interfaces and free boundaries, Tome 26 (2024) no. 3, pp. 321-380. doi: 10.4171/ifb/507
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     title = {Almost minimizers for the thin obstacle problem with variable coefficients},
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     pages = {321--380},
     year = {2024},
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     doi = {10.4171/ifb/507},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/507/}
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