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Viscosity solutions of fully nonlinear, local or non local, Hamilton-Jacobiequations with a super-quadratic growth in the gradient variable are proved tobe H\"older continuous, with a modulus depending only on the growth of theHamiltonian. The proof involves some representation formula for nonlocalHamilton-Jacobi equations in terms of controlled jump processes and a weakreverse inequality.

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