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A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable

Published online by Cambridge University Press:  28 March 2008

Pierre Cardaliaguet
Pierre Cardaliaguet*
Affiliation:
Laboratoire de Mathématiques, UMR 6205, Université de Bretagne Occidentale, 6 Av. Le Gorgeu, BP 809, 29285 Brest, France; Pierre.Cardaliaguet@univ-brest.fr
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Abstract

We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally Hölder continuous with Hölder exponent depending only on the growth of the Hamiltonian. The proof relies on a reverse Hölder inequality.

Keywords

Hamilton-Jacobi equationviscosity solutionsoptimal controlregularityreverse Hölder inequality
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 2 , April 2009 , pp. 367 - 376
Copyright
© EDP Sciences, SMAI, 2008

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References

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