Related papers: Constrained minimum Riesz energy problems for a co…

The study of singular perturbations of the Dirichlet energy is at the core of the phenomenological-description paradigm in soft condensed matter. Being able to pass to the limit plays a crucial role in the understanding of the…

The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional defined on the space of vector fields $H^1(S,T)$, where $S$ and $T$ are surfaces of revolution. The energy functional we consider is closely related…

We consider a non-local interaction energy over bounded densities of fixed mass $m$. We prove that under certain regularity assumptions on the interaction kernel these energies admit minimizers given by characteristic functions of sets when…

We study properties of the $\alpha$-Green kernel $g_D^\alpha$ of order $0<\alpha\leqslant2$ for a domain $D\subset\mathbb R^n$, $n\geqslant3$. This kernel is associated with the $\alpha$-Riesz kernel $|x-y|^{\alpha-n}$, $x,y\in\mathbb R^n$,…

For the $\alpha$-Green kernel $g^\alpha_D$ on a domain $D\subset\mathbb R^n$, $n\geqslant2$, associated with the $\alpha$-Riesz kernel $|x-y|^{\alpha-n}$, where $\alpha\in(0,n)$ and $\alpha\leqslant2$, and a relatively closed set $F\subset…

We consider the minimization of an energy functional given by the sum of a density perimeter and a nonlocal interaction of Riesz type with exponent $\alpha$, under volume constraint, where the strength of the nonlocal interaction is…

We consider the minimization of an energy functional given by the sum of a crystalline perimeter and a nonlocal interaction of Riesz type, under volume constraint. We show that, in the small mass regime, if the Wulff shape of the…

We investigate a homogenization problem related to a non-local interface energy with a periodic forcing term. We show the existence of planelike minimizers for such energy. Moreover, we prove that, under suitable assumptions on the…

We have studied the configurations of minimal energy of $N$ charges on a curve on the plane, interacting with a repulsive potential $V_{ij} = 1/r_{ij}^s$, with $s \geq 1$ and $i,j=1,\dots, N$. Among the examples considered are ellipses of…

We obtain new asymptotic results about systems of $ N $ particles governed by Riesz interactions involving $ k $-nearest neighbors of each particle as $N\to\infty$. These results include a generalization to weighted Riesz potentials with…

Let A be a compact set in the right-half plane and $\Gamma(A)$ the set in $\mathbb{R}^{3}$ obtained by rotating A about the vertical axis. We investigate the support of the limit distribution of minimal energy point charges on $\Gamma(A)$…

We examine lower order perturbations of the harmonic map prob- lem from $\mathbb{R}^2$ to $\mathbb{S}^2$ including chiral interaction in form of a helicity term that prefers modulation, and a potential term that enables decay to a uniform…

We establish an energy quantization for constrained Willmore surfaces, where the constraints are given by area, volume, and total mean curvature, assuming that the underlying conformal structures remain bounded. Furthermore, we show strong…

We investigate properties of minimal $N$-point Riesz $s$-energy on fractal sets of non-integer dimension, as well as asymptotic behavior of $N$-point configurations that minimize this energy. For $s$ bigger than the dimension of the set…

This paper extends the theory of rough convergence from normed linear spaces to the more abstract setting of Riesz spaces. We introduce and systematically develop the concept of rough $\mathbb{c}$-convergence ($rc$-convergence) for nets. A…

We derive Adams inequalities for potentials on general measure spaces, extending and improving previous results obtained by the authors. The integral operators involved, which we call "Riesz subcritical", have kernels whose decreasing…

We study the computational complexity of exact cardinality-constrained minimum Riesz $s$-energy subset selection in finite metric spaces: given $n$ points, select $k<n$ points of minimum Riesz $s$-energy. The objective sums inverse-power…

Given a compact Riemannian manifold $(M^n,g)$ and a fixed cohomology class, $[\alpha^*] \in H^k(M)$, we consider the existence of a minimizer $\alpha \in [\alpha^*]$ of the generalized minimal surface energy $\int_M \sqrt{1+|\alpha|^2}…

We study investigate a long, thin rectangular elastic membrane that is bent through an angle $2 \alpha$, using the Foppl--von Karman ansatz in a geometrically linear setting. We study the associated variational problem, and show the…

We consider the minimization problem of an anisotropic energy in classes of $d$-rectifiable varifolds in $\mathbb R^n$, closed under Lipschitz deformations and encoding a suitable notion of boundary. We prove that any minimizing sequence…