Ricerc@Sapienza

We built sign-changing solutions for a linear perturbation of the classical Yamabe problem.

Motivated by the statistical mechanics description of stationary 2D-turbulence, for a sinh-Poisson type equation with asymmetric nonlinearity, we construct a concentrating solution sequence in the form of a tower of singular Liouville bubbles, each of which has a different degeneracy exponent. The asymmetry parameter $??(0, 1]$ corresponds to the ratio between the intensity of the negatively rotating vortices and the intensity of the positively rotating vortices.

We prove the existence of solutions to a linear perturbation of the classical Yamabe problem, which look like the superposition of k positive bubbles
centered at a suitable point of the manifold.

We consider the Cauchy problem for two prototypes of flux-saturated diffusion equations. In arbitrary space dimension, we give an optimal condition on the growth of the initial datum which discriminates between occurrence or nonoccurrence of a waiting time phenomenon. We also prove optimal upper bounds on the waiting time. Our argument is based on the introduction of suitable families of subsolutions and on a comparison result for a general class of flux-saturated diffusion equations.

In this paper we study the tail behavior of Mexican needlets, a class of spherical wavelets introduced by Geller and Mayeli in [12]. More specifically, we provide an explicit upper bound depending on the resolution level j and a parameter s governing the shape of the Mexican needlets.

We consider planar skew Brownian motion (BM) across pre-fractal Koch interfaces $\partial \Omega_n$ and moving on $\Omega^\epsilon_n = \Sigma_n \cup \Omega_n$. We study the asymptotic behaviour of the corresponding multiplicative additive functionals when thickness of $\Sigma_n$ and skewness coefficients vanish with different rates.

Given an action ? of a discrete group G on a unital C?-algebra A, we
introduce a natural concept of ?-negative definiteness for functions from G to A,
and examine some of the first consequences of such a notion. In particular, we prove
analogs of theorems due to Delorme–Guichardet and Schoenberg in the classical case
where A is trivial. We also give a characterization of the Haagerup property for the
action ? when G is countable.

Aim of this note is to study the infinity Laplace operator and the corresponding Absolutely Minimizing Lipschitz Extension problem on the Sierpinski gasket in the spirit of the classical construction of Kigami for the Laplacian. We introduce a notion of infinity harmonic functions on pre-fractal sets and we show that these functions solve a Lipschitz extension problem in the discrete setting. Then we prove that the limit of the infinity harmonic functions on the pre-fractal sets solves the Absolutely Minimizing Lipschitz Extension problem on the Sierpinski gasket.

We propose a numerical method for stationary Mean Field Games defined on a network.
In this framework a correct approximation of the transition conditions at the vertices plays a crucial
role. We prove existence, uniqueness and convergence of the scheme and we also propose a least squares
method for the solution of the discrete system. Numerical experiments are carried out.

An analytical comparison of a flow SPR immunosensor method and a conventional amperometric immunosensor has been carried out. Different formats were used, respectively, main analytical data have been checked and affinity constant values evaluated and compared.