Double Obstacle Problems with Obstacles Given by Non-C-2 Hamilton-Jacobi Equations
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
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.
Elastic-Plastic Torsion, Viscosity Solutions, Inequalities
IdentifiersURN: urn:nbn:se:kth:diva-105635DOI: 10.1007/s00205-012-0541-4ISI: 000310317200003ScopusID: 2-s2.0-84868153835OAI: oai:DiVA.org:kth-105635DiVA: diva2:572203
FunderSwedish Research Council
QC 201211272012-11-272012-11-232012-11-27Bibliographically approved