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Almost minimizers for the thin obstacle problem with variable coefficients
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-7172-5293
Purdue Univ, Dept Math, 150 N Univ St, W Lafayette, IN 47907 USA..
Western Washington Univ, Dept Math, 516 High St, Bellingham, WA 98225 USA..
2024 (English)In: Interfaces and free boundaries (Print), ISSN 1463-9963, E-ISSN 1463-9971, Vol. 26, no 3, p. 321-380Article in journal (Refereed) Published
Abstract [en]

We study almost minimizers for the thin obstacle problem with variable Holder continuous coefficients and zero thin obstacle, and establish their C-1,C-beta. 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.

Place, publisher, year, edition, pages
European Mathematical Society - EMS , 2024. Vol. 26, no 3, p. 321-380
Keywords [en]
almost minimizers, thin obstacle problem, Signorini problem, Weiss-type monotonicity formula, Almgren's frequency formula, regular set, singular set
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-350475DOI: 10.4171/IFB/507ISI: 001258909100001Scopus ID: 2-s2.0-85197381589OAI: oai:DiVA.org:kth-350475DiVA, id: diva2:1884267
Note

QC 20240715

Available from: 2024-07-15 Created: 2024-07-15 Last updated: 2024-07-22Bibliographically approved

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Jeon, Seongmin

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