Related papers: Universal optimal configurations for the $p$-frame…
We give necessary and sufficient conditions for minimality of generalized minimizers for linear-growth functionals of the form \[ \mathcal F[u] := \int_\Omega f(x,u(x)) \, \text{d}x, \qquad u:\Omega \subset \mathbb R^N\to \mathbb R^d, \]…
We obtain Lipschitz estimates for bounded minimizers of functionals with nonstandard $(p,q)$-growth satisfying the dimension-independent restriction $q<p+2$ with $p \geq 2$. This relation improves existing restrictions when $p \leq N-1$,…
We study the problem of minimizing the second Dirichlet eigenvalue for the Laplacian operator among sets of given perimeter. In two dimensions, we prove that the optimum exists, is convex, regular, and its boundary contains exactly two…
We investigate the existence of approximation algorithms for maximization of submodular functions, that run in fixed parameter tractable (FPT) time. Given a non-decreasing submodular set function $v: 2^X \to \mathbb{R}$ the goal is to…
Recently, the authors of \cite{SYZ22} developed a neural network with width $36d(2d + 1)$ and depth $11$, which utilizes a special activation function called the elementary universal activation function, to achieve the super approximation…
We investigate local minimizers of Ginzburg--Landau-type functionals in dimension $n\geq 3$ that satisfy logarithmic energy bounds, assuming the potential has a vacuum manifold with a finite fundamental group. We show that the normalized…
In this paper, we investigate the concept of p-convexity for sets and functions in n-dimensional Euclidean space. We establish novel algebraic and topological results within this generalized convexity framework. Furthermore, we analyze…
Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. Maximization of such functions subject to various constraints receives little…
A uniform tight frame of N vectors for a d dimensional space is correlation minimizing if among all such frames it is as "nearly" orthogonal as possible, i.e., it minimizes the maximal inner product of unequal vectors. In this paper we…
We investigate the convergence as $p\searrow1$ of the minimizers of the $W^{s,p}$-energy for $s\in(0,1)$ and $p\in(1,\infty)$ to those of the $W^{s,1}$-energy, both in the pointwise sense and by means of $\Gamma$-convergence. We also…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
In this paper we provide density estimates for a class of functions which includes all the minimizers of the energy $\mathcal{E}_s^p(u,\Omega):=(1-s)\left(\frac{1}{2}\int_{\Omega}\int_{\Omega}\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}\,dx\,dy…
We study the $L^p$ concentration problem for the Born--Jordan distribution in dimension $d>1$, thus extending the one-dimensional analysis in [Stra-Svela-Trapasso, J. Math. Pures Appl. (2026)]. We show that the existence of concentration…
We analyze the evolution of the effective potential and the particle spectrum of two-parameter families of non-integrable quantum field theories. These theories are defined by deformations of conformal minimal models M_m by using the…
Consider the supremal functional \[ \tag{1} \label{1} E_\infty(u,A) \,:=\, \|L(\cdot,u,D u)\|_{L^\infty(A)},\quad A\subseteq \Omega, \] applied to $W^{1,\infty}$ maps $u:\Omega\subseteq \mathbb{R}\longrightarrow \mathbb{R}^N$, $N\geq 1$.…
We study three restrictions on normalizers or centralizers in finite p-groups, namely: (i) |N_G(H) : H| <= p^k for every H non-normal in G, (ii) |N_G(<g>) : <g>| <= p^k for every <g> non-normal in G, and (iii) |C_G(g) : <g>| <= p^k for…
We prove existence and uniqueness of minimizers for a family of energy functionals that arises in Elasticity and involves polyconvex integrands over a certain subset of displacement maps. This work extends previous results by Awi and Gangbo…
Motivated by the construction of confidence intervals in statistics, we study optimal configurations of $2^d-1$ lines in real projective space $RP^{d-1}$. For small $d$, we determine line sets that numerically minimize a wide variety of…
We study the limiting behavior of minimizing $p$-harmonic maps from a bounded Lipschitz domain $\Omega \subset \mathbb{R}^{3}$ to a compact connected Riemannian manifold without boundary and with finite fundamental group as $p \nearrow 2$.…
Consider the class of zero-mean functions with fixed $L^{\infty}$ and $L^1$ norms and exactly $N\in \mathbb{N}$ nodal points. Which functions $f$ minimize $W_p(f_+,f_-)$, the Wasserstein distance between the measures whose densities are the…