Hölder continuity to Hamilton-Jacobi equations with superquadratic growth in the gradient and unbounded right-hand side

Pierre Cardaliaguet (1) , Luis Silvestre (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Department of Mathematics [Chicago]

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.

Domaines: Equations aux dérivées partielles [math.AP]

Pierre Cardaliaguet, Luis Silvestre. Hölder continuity to Hamilton-Jacobi equations with superquadratic growth in the gradient and unbounded right-hand side. Communications in Partial Differential Equations, 2012, 37 (9), pp.1668-1688. ⟨10.1080/03605302.2012.660267⟩. ⟨hal-00633218⟩