De Giorgi Techniques Applied to The Holder Regularity of Solutions to   Hamilton-Jacobi Equations
  This article is dedicated to the proof of C^{\alpha} regularization effects of Hamilton- Jacobi equations. The proof is based on the De Giorgi method. The regularization is independent on the regularity of the Hamiltonian. 
Chi Hin Chan and Alexis F. Vasseur
math.AP