Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T18:51:21.836Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the regularity of solutionsof Hamilton-Jacobi equations with superlinear growthin 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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

M. Bardi and I. Capuzzo Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Birkhäuser (1996).
Barles, G., Regularity results for first order Hamilton-Jacobi equations. Differ. Integral Equ. 3 (1990) 103–125.
G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi. Springer-Verlag, Berlin (1994).
A. Bensoussan and J. Frehse, Regularity results for nonlinear elliptic systems and applications, Applied Mathematical Sciences 151. Springer-Verlag, Berlin (2002).
Gehring, F.W., The Lp -integrability of the partial derivatives of a quasiconformal mapping. Acta Math. 130 (1973) 265–277. CrossRef
Lions, P.-L., Regularizing effects for first-order Hamilton-Jacobi equations. Applicable Anal. 20 (1985) 283–307. CrossRef
Rampazzo, F. and Sartori, C., Hamilton-Jacobi-Bellman equations with fast gradient-dependence. Indiana Univ. Math. J. 49 (2000) 1043–1077. CrossRef