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

Cardaliaguet, Pierre (2009), A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable, ESAIM. COCV, 15, 2, p. 367-376. http://dx.doi.org/10.1051/cocv:2008028

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/0802.3153v1
Date
2009
Journal name
ESAIM. COCV
Volume
15
Number
2
Publisher
EDP Sciences
Pages
367-376
Publication identifier
Metadata
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Author(s)
Cardaliaguet, Pierre
Abstract (EN)
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.
Subjects / Keywords
Hamilton-Jacobi equation; viscosity solutions; optimal control; regularity; reverse Hölder inequality