H\"older continuity to Hamilton-Jacobi equations with superquadratic   growth in the gradient and unbounded right-hand side
  We show that solutions of time-dependent degenerate parabolic equations with super-quadratic growth in the gradient variable and possibly unbounded right-hand side are locally ${\mathcal C}^{0,\alpha}$. Unlike the existing (and more involved) proofs for equations with bounded right-hand side, our arguments rely on constructions of sub- and supersolutions combined with improvement of oscillation techniques. 
Pierre Cardaliaguet (CEREMADE), Luis Silvestre
math.AP