Alessandra Cutrì

On the Liouville property for fully nonlinear equations

Abstract In this paper we prove some Liouville theorems for nonnegative viscosity supersolutions of a class of fully nonlinear uniformly elliptic problems in R N .

Liouville theorems for semilinear equations on the Heisenberg group

Abstract In this paper we consider problems of the type Δ H u + h(ϰ)u p ⩾ 0, in D ⊂ R 2n + 1 u≥0 in D , where ΔH is the Heisenberg Laplacian, D is an unbounded domain and h is a non negative function. We prove that, under suitable conditions on h, p and D, the only solution of (1) is u ≡ 0.

Hadamard and Liouville Type Results for Fully Nonlinear Partial Differential Inequalities

In this paper we prove some Hadamard and Liouville type properties for nonnegative viscosity supersolutions of fully nonlinear uniformly elliptic partial differential inequalities in the whole space.

Hamilton-Jacobi equations on networks

We consider continuous-state and continuous-time control problem where the admissible trajectories of the system are constrained to remain on a network. Under suitable assumptions, we prove that the value function is continuous. We define a notion of viscosity solution of Hamilton-Jacobi equations on the network for which we prove a comparison principle. The value function is thus the unique viscosity solution of the Hamilton-Jacobi equation on the network.