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Double obstacle problems with obstacles given by non-C 2 Hamilton–Jacobi equations
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Andersson, John Erik, Shahgholian, Henrik and Weiss, Georg S. (2012) Double obstacle problems with obstacles given by non-C 2 Hamilton–Jacobi equations. Archive for Rational Mechanics and Analysis, Vol.206 (No.3). pp. 779-819. doi:10.1007/s00205-012-0541-4
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Official URL: http://dx.doi.org/10.1007/s00205-012-0541-4
Abstract
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.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Archive for Rational Mechanics and Analysis | ||||
| Publisher: | Springer | ||||
| ISSN: | 0003-9527 | ||||
| Official Date: | December 2012 | ||||
| Dates: |
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| Volume: | Vol.206 | ||||
| Number: | No.3 | ||||
| Page Range: | pp. 779-819 | ||||
| DOI: | 10.1007/s00205-012-0541-4 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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