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

Pierre Cardaliaguet (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Domaines: Optimisation et contrôle [math.OC]

Pierre Cardaliaguet. A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable. ESAIM: Control, Optimisation and Calculus of Variations, 2009, 15 (2), pp.367-376. ⟨hal-00258297⟩