In this paper we investigate the validity and the consequences of the maximum principle for
degenerate elliptic operators whose higher order term is the sum of k eigenvalues of the …

Regularity and uniqueness of the first eigenfunction for singular fully nonlinear operators Page
1 J. Differential Equations 249 (2010) 1089–1110 Contents lists available at ScienceDirect …

Let g 0 be a smooth Riemannian metric on a closed manifold M n of dimension n≥ 3. We
study the existence of a smooth metric g conformal to g 0 whose Schouten tensor A g …

We prove the existence of two fundamental solutions Φ and ̃Φ of the PDE\input amssym F
(D^ 2 Φ)= 0\rm in {R^ n ∖ {0\} for any positively homogeneous, uniformly elliptic operator F …

We characterize the validity of the Maximum Principle in bounded domains for fully
nonlinear degenerate elliptic operators in terms of the sign of a suitably defined generalized …

We extend the Caffarelli-Świech-Winter C 1, α regularity estimates to L p-viscosity solutions
of fully nonlinear uniformly elliptic equations in nondivergence form with superlinear growth …

We develop a new, unified approach to the following two classical questions on elliptic
PDE:• the strong maximum principle for equations with non-Lipschitz nonlinearities,• the at …

F (D2u)= up, p> 1, in Rn or in exterior domains, where F is any uniformly elliptic, positively
homogeneous operator. We show that there exists a critical exponent, depending on the …

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic
equations near boundary points of Lipschitz domains at which the solution may be singular …

Zero-sum games with risk-sensitive cost criterion are considered with underlying dynamics
being given by controlled stochastic differential equations. Under the assumption of …