A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable
Laboratoire de Mathématiques, UMR 6205, Université de Bretagne
Occidentale, 6 Av. Le Gorgeu,
BP 809, 29285 Brest, France; Pierre.Cardaliaguet@univ-brest.fr
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.
Mathematics Subject Classification: 35F20 / 49L25
Key words: Hamilton-Jacobi equation / viscosity solutions / optimal control / regularity / reverse Hölder inequality
© EDP Sciences, SMAI, 2008