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Optimal regularity for the Signorini problem and its free boundary
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2015 (English)In: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297Article in journal (Refereed) Epub ahead of print
Abstract [en]

We will show optimal regularity for minimizers of the Signorini problem for the Lame system. In particular if (Formula presented.) minimizes (Formula presented.)in the convex set (Formula presented.)where (Formula presented.) say. Then (Formula presented.). Moreover the free boundary, given by (Formula presented.)will be a (Formula presented.) graph close to points where (Formula presented.) is not degenerate. Similar results have been know before for scalar partial differential equations (see for instance [5, 6]). The novelty of this approach is that it does not rely on maximum principle methods and is therefore applicable to systems of equations.

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URN: urn:nbn:se:kth:diva-175031DOI: 10.1007/s00222-015-0608-6ScopusID: 2-s2.0-84932153128OAI: diva2:876547

QP 201512

Available from: 2015-12-04 Created: 2015-10-09 Last updated: 2015-12-04Bibliographically approved

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