Existence and regularity results for fully nonlinear equations with singularities

Patricio Felmer (1) , Alexander Quaas (2) , Boyan Sirakov (3)

1 DIM - Departamento de Ingenieria Matematica and Centro de Modelamiento Matematico
2 Departamento de Matematica [Valparaiso]
3 MODAL'X - Modélisation aléatoire de Paris X

In this paper we consider the Dirichlet boundary value problem for a singular elliptic PDE lke $F[u] = p(x)u^{-\mu}$, where $p,\mu\ge 0$, in a bounded smooth domain in $\mathbb{R}^n$. The nondivergence form operator $F$ is assumed to be of Hamilton-Jacobi-Bellman or Isaacs type. We establish existence and regularity results for such equations.

Domaines: Equations aux dérivées partielles [math.AP]

Patricio Felmer, Alexander Quaas, Boyan Sirakov. Existence and regularity results for fully nonlinear equations with singularities. Mathematische Annalen, 2012, 354 (1), pp.377-400. ⟨hal-00462082v2⟩