Enrico Jannelli

The Hyperbolic Symmetrizer: Theory and Applications

The hyperbolic symmetrizer is a matrix which symmetrizes in a standard way any Sylvester hyperbolic matrix. This paper deals with the theory of the hyperbolic symmetrizer, its relationships with the concept of Bezout matrix, its perturbations which originate the so–called quasi-symmetrizer and its applications to Cauchy problems for linear weakly hyperbolic equations.

Dissipative higher order hyperbolic equations

ABSTRACT In this paper, we describe a constructive method to find a dissipative term for any generic higher order, homogeneous, possibly weakly, hyperbolic operator , with x∈ℝn, n≥1. We derive long-time decay estimates for the solution to the related Cauchy problem. We provide an example of application to the theory of elastic waves.

Nonlinear Elliptic Problems Involving Critical Sobolev Exponent in the Case of Symmetrical Domains

We consider the boundary value problem

On the Symmetrization of the Principal Symbol of Hyperbolic Equations

(*)\,\,\,\,\,\,\,\,\,\,\, - \Delta \,u\,\,\,\, - \,\,\lambda u\, - \,u{\left| u \right|^{2* - 2}}\, = \,0\,\,\,\,u\,\varepsilon \,H\begin{array}{*{20}{c}} 1 \\ 0 \end{array}\,(\Omega )

Ar kovalevskian systems with time-dependent coefficients

where Ω ⊂ ℝn is a bounded domain, n ⩾ 4, 2* = 2n/(n − 2) is the critical exponent for the Sobolev embedding and λ is a real positive parameter. We state some theorems which ensure the existence of infinitely many solutions of (*) when Ω exhibits suitable simmetries.