Comparison principle and Liouville type results for singular fully nonlinear operators

Harnack inequality for singular fully nonlinear operators and some existence results

“…In Theorem 1.1 the notion of solution is that introduced by Chen et al in [14] and Evans and Spruck in [22] for singular problems and adopted by Birindelli and Demengel in [2]- [5]. This is a variation of the usual notion of viscosity solution for (1.1), that takes into account that we cannot test functions with vanishing gradient at the testing point.…”

“…1.1 with α > −1, was initiated in a series of papers by Birindelli and Demengel [2][3][4][5][6]. With an appropriate notion of solution an existence theory for the Dirichlet boundary value problem based on Perron's method is developed.…”

Global $$W^{2,\delta }$$ W 2 , δ estimates for a type of singular fully nonlinear elliptic equations

“…The investigation of equations of this type has made much progress in recent years. I. Birindelli and F. Demengel proved comparison principle [BD04] and C 1,α estimate [BD10]. G. Dávila, P. Felmer and A. Quaas proved Alexandroff-Bakelman-Pucci (ABP for short) estimate [DFQ09] and Harnack inequality [DFQ10].…”

A note on the Liouville method applied to elliptic eventually degenerate fully nonlinear equations governed by the Pucci operators and the Keller–Osserman condition

“…We note that the presence of a strong absorption term enables us to derive this version of the Liouville Theorem independent on the dimension. See also [1] were a comparison principle in the whole space is obtained.…”