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Double Obstacle Problems with Obstacles Given by Non-C-2 Hamilton-Jacobi Equations
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2012 (English)In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 206, no 3, 779-819 p.Article in journal (Refereed) Published
Abstract [en]

We prove optimal regularity for double obstacle problems when obstacles are given by solutions to Hamilton-Jacobi equations that are not C (2). When the Hamilton-Jacobi equation is not C (2) then the standard Bernstein technique fails and we lose the usual semi-concavity estimates. Using a non-homogeneous scaling (different speeds in different directions) we develop a new pointwise regularity theory for Hamilton-Jacobi equations at points where the solution touches the obstacle. A consequence of our result is that C (1)-solutions to the Hamilton-Jacobi equation <Equation ID="Equa"> <MediaObject> </MediaObject> </Equation>, are, in fact, C (1,alpha/2), provided that . This result is optimal and, to the authors' best knowledge, new.

Place, publisher, year, edition, pages
2012. Vol. 206, no 3, 779-819 p.
Keyword [en]
Elastic-Plastic Torsion, Viscosity Solutions, Inequalities
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-105635DOI: 10.1007/s00205-012-0541-4ISI: 000310317200003Scopus ID: 2-s2.0-84868153835OAI: oai:DiVA.org:kth-105635DiVA: diva2:572203
Funder
Swedish Research Council
Note

QC 20121127

Available from: 2012-11-27 Created: 2012-11-23 Last updated: 2017-12-07Bibliographically approved

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Shahgholian, Henrik

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