Double obstacle problems with obstacles given by non-C 2 Hamilton–Jacobi equations
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. ISSN 0003-9527Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/s00205-012-0541-4
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 > Mathematics|
|Journal or Publication Title:||Archive for Rational Mechanics and Analysis|
|Official Date:||December 2012|
|Page Range:||pp. 779-819|
|Access rights to Published version:||Restricted or Subscription Access|
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