Solvability of uniformly elliptic fully nonlinear PDE

Boyan Sirakov (1, 2)

1 MODAL'X - Modélisation aléatoire de Paris X
2 CAMS - Centre d'Analyse et de Mathématique sociales

We get existence, uniqueness and non-uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of Hamilton-Jacobi-Bellman-Isaacs type, with unbounded ingredients and quadratic growth in the gradient, without hypotheses of convexity or properness. Some of our results are new even for equations in divergence form.

Domaines: Equations aux dérivées partielles [math.AP]

Boyan Sirakov. Solvability of uniformly elliptic fully nonlinear PDE. Archive for Rational Mechanics and Analysis, 2010, 195 (2), pp.579-607. ⟨hal-00115525v3⟩