Hölder regularity for viscosity solutions of fully nonlinear, local or nonlocal, Hamilton-Jacobi equations with super-quadratic growth in the gradient

Pierre Cardaliaguet (1) , Catherine Rainer (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LM - Laboratoire de mathématiques de Brest

Viscosity solutions of fully nonlinear, local or non local, Hamilton-Jacobi equations with a super-quadratic growth in the gradient variable are proved to be Hölder continuous, with a modulus depending only on the growth of the Hamiltonian. The proof involves some representation formula for nonlocal Hamilton-Jacobi equations in terms of controlled jump processes and a weak reverse inequality.

Mots clés: reverse Hölder inequalities; Integro-Differential Hamilton-Jacobi equations; viscosity solutions; Hölder continuity; degenerate parabolic equations; reverse Hölder inequalities.

Domaines: Optimisation et contrôle [math.OC]

Pierre Cardaliaguet, Catherine Rainer. Hölder regularity for viscosity solutions of fully nonlinear, local or nonlocal, Hamilton-Jacobi equations with super-quadratic growth in the gradient. SIAM Journal on Control and Optimization, 2011, 49 (2), pp.555-573. ⟨hal-00451248⟩