Abstract. The functionality of the visual cortex has been described in [63] and in [50] as a contact manifold of dimension three and in [62] the Mumford and Shah functional has been proposed toâ€¦ (More)

Aim of this study is to provide a formal link between connectionist neural models and variational psycophysical ones. We show that the solution of phase difference equation of weakly connected neuralâ€¦ (More)

Minimal surfaces in the sub-Riemannian Heisenberg group can be constructed by means of a Riemannian approximation scheme, as limit of Riemannian minimal surfaces. We study the regularity ofâ€¦ (More)

The aim of this paper is to provide a formal link between an oscillatory neural model, whose phase is represented by a difference equation, and the Mumford and Shah functional. A Riemannian metric isâ€¦ (More)

We prove that Lipschitz intrinsic graphs in the Heisenberg groups H, with n > 1, which are vanishing viscosity solutions of the minimal surface equation, are smooth and satisfy the PDE in a strongâ€¦ (More)

We characterize intrinsic Lipschitz functions as maps which can be approximated by a sequence of smooth maps, with pointwise convergent intrinsic gradient. We also provide an estimate of theâ€¦ (More)

We prove that Lipschitz intrinsic graphs in the Heisenberg groups Hn, with n > 1, which are vanishing viscosity solutions of the minimal surface equation are smooth.

We prove some maximum and gradient estimates for classical solutions to a wide class of quasilinear degenerate parabolic equations, including first order ones. The proof is elementary and exploitsâ€¦ (More)

We prove that Lipschitz intrinsic graphs in the Heisenberg groups H , with n > 1, which are vanishing viscosity solutions of the minimal surface equation are smooth.

We prove that Lipschitz intrinsic graphs in the Heisenberg groups Hn, with n > 1, which are vanishing viscosity solutions of the minimal surface equation are smooth.