Hölder Regularity for Viscosity Solutions of Fully Nonlinear, Local or Nonlocal, Hamilton-Jacobi Equations with Superquadratic Growth in the Gradient

Authors:
Pierre Cardaliaguet;Catherine Rainer
Affiliations:
cardaliaguet@ceremade.dauphine.fr;Catherine.Rainer@univ-brest.fr
Venue:
SIAM Journal on Control and Optimization
Year:
2011

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SIAM Journal on Control and Optimization

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Abstract

Viscosity solutions of fully nonlinear, local or nonlocal, Hamilton-Jacobi equations with a superquadratic 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 Hölder inequality.