Alberto Ferrero

Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential

Asymptotics of solutions to Schroedinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis-Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with a homogeneity of order -1.

On a fourth order Steklov eigenvalue problem

Summary We study the spectrum of a biharmonic Steklov eigenvalue problem in a bounded domain of Rn. We characterize it in general and give its explicit form in the case where the domain is a ball. Then, we focus our attention on the first eigenvalue of this problem. We prove some estimates and study its isoperimetric properties. By recalling a number of known results, we finally highlight the main open problems still to be solved.

Existence and multiplicity results for semilinear equations with measure data

In this paper, we study existence and nonexistence of solutions for the Dirichlet problem associated with the equation

Almgren-type monotonicity methods for the classification of behaviour at corners of solutions to semilinear elliptic equations

-\Delta u=g(x,u)+\mu

Existence and multiplicity results for semilinear ellipctic equations with measure data and jumping nonlinearities

where

Asymptotic behavior of ground states of quasilinear elliptic problems with two vanishing parameters, Part III

\mu

Existence of Solutions for Singular Critical Growth Semilinear Elliptic Equations

is a Radon measure. Existence and nonexistence of solutions strictly depend on the nonlinearity

DECAY AND EVENTUAL LOCAL POSITIVITY FOR BIHARMONIC PARABOLIC EQUATIONS

g(x,u)

A partially hinged rectangular plate as a model for suspension bridges

and suitable growth restrictions are assumed on it. Our proofs are obtained by standard arguments from critical theory and in order to find solutions of the equation, suitable functionals are introduced by mean of approximation arguments and iterative schemes.

Supercritical biharmonic equations with power-type nonlinearity

A monotonicity approach to the study of the asymptotic behavior near corners of solutions to semilinear elliptic equations in domains with a conical boundary point is discussed. The presence of logarithms in the first term of the asymptotic expansion is excluded for boundary profiles sufficiently close to straight conical surfaces.