Research
Research
Research
Research
69+ open-access research outputs.
In the present survey, we consider the classical reinforcement problem for elliptic boundary value problems originally studied by Sanchez-Palencia in 1969. We focus on the seminar papers by Brezis, Ca…
This white paper presents a critical synthesis of the recent breakthrough in nonuniformly elliptic regularity theory and the burgeoning field of neurosymbolic large reasoning models (LRMs). We explore…
For a fixed, compactly supported probability measure $\mu$ on the $d$-dimensional space $\mathbb{R}^d$, we consider the problem of minimizing the $p^{\mathrm{th}}$-power average distance functional ov…
The history of the Arcetri Institute of Physics at the University of Florence is analyzed from the beginning of the 20th century to the 1960s. Thanks to the arrival of Garbasso in 1913, not only did t…
The creation of artificial polyglot voices remains a challenging task, despite considerable progress in recent years. This paper investigates self-supervised learning for voice conversion to create na…
In a previous work \cite{Buttazzo:2020ibd}, it has been pointed out that heavy new physics (NP) contributions to lepton dipole moments and high-energy cross-sections of lepton pairs into Higgs and $\g…
We study pencils of plane cubics with only one base point and general member smooth, giving a complete classification. Under the additional hypothesis that all members are irreducible, we prove that t…
We refer here to the surprising construction made by Giuseppe Peano in 1890. He gave an example of a continuous function (called now the Peano curve) from the unit interval to the whole unit square. W…
In this manuscript we investigate the equivalence of Fourier-based metrics on discrete state spaces with the well-known Wasserstein distances. While the use of Fourier-based metrics in continuous stat…
We prove a lower bound for the Cheeger constant of a cylinder $\Omega\times (0,L)$, where $\Omega$ is an open and bounded set. As a consequence, we obtain existence of minimizers for the shape functio…
In this paper, we prove estimates on the dimension of the singular part of the free boundary for solutions to shape optimization problems with measure constraints. The focus is on the heat conduction …
Let $\Omega\subset\mathbb{R}^n$ be an open set with the same volume as the unit ball $B$ and let $\lambda_k(\Omega)$ be the $k$-th eigenvalue of the Laplace operator of $\Omega$ with Dirichlet boundar…
The folder containing the sheets of the Memoirs of Dilworth/Occhialini is kept in the Dilworth-Occhialini Archives at the BICF Library of the University of Milan. They cover the two English periods of…
Let $\Omega$ be a bounded Lipshcitz domain in $\mathbb{R}^n$ and we study boundary behaviors of solutions to the Laplacian eigenvalue equation with constant Neumann data. \begin{align} \label{cequat…
We examine $L^p$-viscosity solutions to fully nonlinear elliptic equations with bounded-measurable ingredients. By considering $p_0<p<d$, we focus on gradient-regularity estimates stemming from nonlin…
The history of the Institute of Physics at the University of Florence is traced from the beginning of the 20th century, with the arrival of Antonio Garbasso as Director (1913), to the 1960s. Thanks to…
We consider the following problem stated in 1993 by Buttazzo and Kawohl: minimize the functional $\int\!\!\int_\Omega (1 + |\nabla u(x,y)|^2)^{-1} dx\, dy$ in the class of concave functions $u: \Omega…
We prove the existence of global minimizers to the double minimization problem \[ \inf\Big\{ P(E) + \lambda W_p(\mathcal{L}^n \lfloor \, E,\mathcal{L}^n \lfloor\, F) \colon |E \cap F| = 0, \, |E| = …
An interesting, yet unknown, episode concerning the effective permeation of the scientific revolution in the XVIII century Kingdom of Naples (and, more generally, Italy) is recounted. The quite intrig…
A refinement of the classic equivalence relation among Cauchy sequences yields a useful infinitesimal-enriched number system. Such an approach can be seen as formalizing Cauchy's sentiment that a null…
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