Related papers: Constrained energy problems with external fields f…
In any dimension $N \geq 1$, for given mass $m > 0$ and for the $C^1$ energy functional \begin{equation*} I(u):=\frac{1}{2}\int_{\mathbb{R}^N}|\nabla u|^2dx-\int_{\mathbb{R}^N}F(u)dx, \end{equation*} we revisit the classical problem of…
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 main focus of this paper is to discuss the solutions of Einstein-Maxwell's field equations for compact stars study. We have chosen the MIT bag model equation of state for the pressure-energy density relationship and conformal Killing…
The constrained minimisers of convex integral functionals of the form $\mathscr F(v)=\int_\Omega F(\nabla^k v(x))\mathrm d x $ defined on Sobolev mappings $v\in \mathrm W^{k,1}_g(\Omega , \mathbb R^N )\cap K$, where $K$ is a closed convex…
The paper deals with the theory of inner (outer) capacities on locally compact spaces with respect to general function kernels, the main emphasis being placed on the establishment of alternative characterizations of inner (outer) capacities…
We study numerically the existence and character of bound states for positive and negative point charges shielded by the response of a two-dimensional homogeneous electron gas. The problem is related to many physical situations and has…
Dynamical scalar fields in an effective four-dimensional field theory are naturally expected to couple to the rest of the theory's degrees of freedom, unless some new symmetry is postulated to suppress these couplings. In particular, a…
In this paper, we introduce several geometric characterizations for strong minima of optimization problems. Applying these results to nuclear norm minimization problems allows us to obtain new necessary and sufficient quantitative…
This paper investigates the existence and qualitative properties of minimizers for a class of nonlocal micromagnetic energy functionals defined on bounded domains. The considered energy functional consists of a symmetric exchange…
We study boundary value problems for bounded uniform domains in $\mathbb{R}^n$, $n\geq 2$, with non-Lipschitz (and possibly fractal) boundaries. We prove Poincar\'e inequalities with trace terms and uniform constants for uniform…
In this paper we study the existence of minimizers for interaction energies with the presence of external potentials. We consider a class of subharmonic interaction potentials, which include the Riesz potentials $|{\bf…
We present a unified, SI-consistent framework to constrain minimal SME coefficients $a_\mu$ and $b_\mu$ using magnetically confined two-dimensional electron systems under a uniform magnetic field. Working in the nonrelativistic…
We study the branch of semi-stable and unstable solutions (i.e., those whose Morse index is at most one) of the Dirichlet boundary value problem $-\Delta u=\frac{\lambda f(x)}{(1-u)^2}$ on a bounded domain $\Omega \subset \R^N$, which…
The power moments of a positive measure on the real line or the circle are characterized by the non-negativity of an infinite matrix, Hankel, respectively Toeplitz, attached to the data. Except some fortunate configurations, in higher…
We investigate Maxwell-scalar models on radially symmetric spacetimes in which the gauge and scalar fields are coupled via the electric permittivity. We find the conditions that allow for the presence of minimum energy configurations. In…
For two continuous and isotropic positive definite kernels on the same compact two-point homogeneous space, we determine necessary and sufficient conditions in order that their product be strictly positive definite. We also provide a…
We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We characterize the semicontinuous envelope of the energy in terms of a…
In this note we study the boundary regularity of minimizers of a family of weak anchoring energies that model the states of liquid crystals. We establish optimal boundary regularity in all dimensions $n\geq 3 .$ In dimension $n=3,$ this…
We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…
We consider volume-constrained minimizers of the fractional perimeter with the addition of a potential energy in the form of a volume inte- gral. Such minimizers are solutions of the prescribed fractional curvature problem. We prove…