Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.57 (2025), 1st Issue

The journal Rendiconti dell’Istituto di Matematica dell’Università di Trieste was founded in 1969 by Arno Predonzan, with the aim of publishing original research articles in all fields of mathematics. Rendiconti dell’Istituto di Matematica dell’Universit`a di Trieste has been the first Italian mathematical journal to be published also on-line. The access to the electronic version of the journal is free. All published articles are available on-line. In 2008 the Dipartimento di Matematica e Informatica, the owner of the journal, decided to renew it. The name of the journal however remained unchanged, but the subtitle An International Journal of Mathematics was added. The journal can be obtained by subscription, or by reciprocity with other similar journals. Currently more than 100 exchange agreements with mathematics departments and institutes around the world have been entered in. The articles published by Rendiconti dell’Istituto di Matematica dell’Universit`a di Trieste are reviewed/indexed by MathSciNet, Zentralblatt Math, Scopus, OpenStarTs.

By using mountain pass arguments and a novel grouptheoretical approach, in this paper we study the existence of multiple sequences of nodal solutions with prescribed different symmetries for a wide class of (sub)critical elliptic problems settled on the unit sphere (Sd, h), of dimension d ≥ 5, whose simple prototype is given by the celebrated Yamabe equation on the sphere.

The paper concerns universal a priori estimates for positive solutions to a large class of elliptic quasilinear equations and systems involving the p-Laplacian operator on arbitrary domains of RN and a convective term in the reaction. Our main theorems, new even for the Laplacian operator, extend previous estimates by Pol´aˇcik, Quitter and Souplet in [38] to very general nonlinearities admitting solely a lower bound, yielding a curious dichotomy. The main ingredients are a key doubling property, a rescaling argument, different from the classical blow-up technique of Gidas and Spruck, and Liouville-type theorems for inequalities. A discussion on the sharpness of the exponent in the power type term is also included.

This research project considers the d-dimensional MagnetoHydroDynamics (MHD) system defined on a sufficiently smooth bounded domain, d = 2, 3 with homogeneous boundary conditions, and subject to external sources assumed to cause instability. The initial conditions for both fluid and magnetic equations are taken of low regularity. We then seek to uniformly stabilize such MHD system in the vicinity of an unstable equilibrium pair, in the critical setting of correspondingly low regularity spaces, by means of explicitly constructed, static, feedback controls, which are localized on an arbitrarily small interior subdomain. In addition, the actuators will be minimal in number. The resulting space of well-posedness and stabilization is a suitable product space eB2−2/p q,p (Ω) × eB2−2/p q,p (Ω), 1 < p < 2q 2q−1 , q > d, of tight Besov spaces for the fluid velocity component and the magnetic field component (each “close” to L3(Ω) for d = 3). It is known that such Besov space does not recognize compatibility conditions at the boundary, yet it provides a “minimal” level of regularity necessary to handle the nonlinear terms. In this paper we provide a solution of the first step: uniform stabilization of the linearized MHD. Showing maximal Lp-regularity up to T = ∞ for the feedback stabilized linearized system is critical for the analysis of well-posedness and stabilization of the feedback nonlinear problem. The solution of the nonlinear stabilization problem is to be given in a successive paper [29].

We prove advanced regularity results for solutions to a sixth order equation arising in the mechanical Kirchhoff-Love’s type model of the static equilibrium of a nanoplate in bending. Such regularity properties play a crucial role in the treatment, among others, of the inverse problem consisting in the determination of the Winkler coefficient of a nanoplate.