Related papers: Equilibrium problems for infinite dimensional vect…
We study the behavior of a general gravitational action, including quadratic terms in the curvature, supplemented by a compact scalar field in 4+1 dimensions. The generalized Einstein equation for this system admits solutions which are…
A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…
We investigate equilibria of charged deformable materials via the minimization of an electroelastic energy. This features the coupling of elastic response and electrostatics by means of a capacitary term, which is naturally defined in…
We study static, spherically symmetric, self-gravitating systems minimally coupled to a scalar field with U(1) gauge symmetry: charged boson stars. We find numerical solutions to the EinsteinMaxwell equations coupled to the relativistic…
We review and assess a part of the recent work on Casimir apparatuses in the weak gravitational field of the Earth. For a free, real massless scalar field subject to Dirichlet or Neumann boundary conditions on the parallel plates, the…
Starting with a static, spherically symmetric spacetime incorporating critical (unstable) closed null geodesics, a family of models for equilibrium states of non-isolated compact objects is obtained by solving the Einstein equations for an…
In this note we study contractivity of monotone systems and exponential convergence of positive systems using non-Euclidean norms. We first introduce the notion of conic matrix measure as a framework to study stability of monotone and…
We study the Dirichlet boundary value problem for equations with absorption of the form $-\Delta u+g\circ u=\mu$ in a bounded domain $\Omega\subset R^N$ where $g$ is a continuous odd monotone increasing function. Under some additional…
This paper investigates the uniqueness of a nonnegative vector solution and the uniqueness of a positive semidefinite matrix solution to underdetermined linear systems. A vector solution is the unique solution to an underdetermined linear…
The paper studies continutity of Moser nonlinearity in two dimensions with respect to weak convergence. Unlike the critical nonlinearity in the Sobolev inequality, which lacks weak continuity at any point, Moser functional fails to be…
We show that the repulsive effects associated to the zero-point energies of quantum fields are capable of supporting ultracompact stars that overcome the compactness limits present in general relativity for any object in hydrostatic…
The stability requirements for a noncommutative scalar field coupled to gravity is investigated through the positive energy theorem. It is shown that for a noncommutative scalar with a polynomial potential, the stability conditions are…
We present several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. We first focus on…
We consider the Cauchy problem for the continuity equation with a bounded nearly incompressible vector field $b\colon (0,T) \times \mathbb R^d \to \mathbb R^d$, $T>0$. This class of vector fields arises in the context of hyperbolic…
Optimizing the free energy under a mass constraint may generate a convex crystal subject to assumptions on the potential $g(0)=0$, $g \ge 0$. The general problem classically attributed to Almgren is to infer if this is the case assuming the…
Under suitable requirements on a kernel on a locally compact space, we develop a theory of inner (outer) balayage of quite general Radon measures $\omega$ (not necessarily of finite energy) onto quite general sets (not necessarily closed).…
In this paper, we consider the electrostatic Born-Infeld model \begin{equation*} \tag{$\mathcal{BI}$} \left\{ \begin{array}{rcll} -\operatorname{div}\left(\displaystyle\frac{\nabla \phi}{\sqrt{1-|\nabla \phi|^2}}\right)&=& \rho & \hbox{in…
We consider the minimum energy problem on the unit sphere $\mathbb S^{d-1}$ in the Euclidean space $\mathbb R^d$, $d\geq 3$, in the presence of an external field $Q$, where the charges are assumed to interact according to Newtonian…
We study the fluctuations of the stress tensor for a massless scalar field in two and four-dimensional Minkowski spacetime in the vacuum state. Covariant expressions for the stress tensor correlation function are obtained as sums of…
We analyze the supports of weighted equilibrium measures in $\mathbb{C}^n$. We give explicit examples of families of compact sets which arise as the support of a weighted equilibrium measure for some admissible weight $w$. These examples…