Related papers: Equilibrium problems for infinite dimensional vect…
We compute the equilibrium measure in dimension d=s+4 associated to a Riesz s-kernel interaction with an external field given by a power of the Euclidean norm. Our study reveals that the equilibrium measure can be a mixture of a continuous…
Voltage instability is a major threat in power system operation. The growing presence of constant power loads significantly aggravates this issue, hence motivating the development of new analysis methods for both existence and stability of…
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…
Gravitational properties of a hedge-hog type topological defect in two extra dimensions are considered in General Relativity employing a vector as the order parameter. All previous considerations were done using the order parameter in the…
The behavior of an electron in an external uniform electromagnetic background coupled to a harmonic potential, with noncommuting space coordinates, is considered in this work. The thermodynamics of the system is studied. Matrix vector…
In this paper, we showed that for some given suitable density and pressure, there exist infinitely many compactly supported solutions with prescribed energy profile. The proof is mainly based on the convex integration scheme. We construct…
We investigate minimum weak $\alpha$-Riesz energy problems with external fields in both the unconstrained and constrained settings for generalized condensers $(A_1,A_2)$ such that the closures of $A_1$ and $A_2$ in $\mathbb R^n$ are allowed…
Single- and multi-valued solutions of homogeneous Maxwell equations in vacuum are considered, with ''sources'' formed by the (point- or string-like) singularities of the field strengths and, generally, irreducible to any delta-functions'…
We prove the existence of equilibrium states for geometric potentials in a class of piecewise weakly convex interval maps. This class includes systems with indifferent fixed points and non-Markov partitions. Under additional hypotheses we…
We consider the inverse problem of determining an electromagnetic potential appearing in an infinite cylindrical domain from boundary measurements. More precisely, we prove the stable recovery of some general class of magnetic field and…
This paper is concerned with stability of the ball for a class of isoperimetric problems under convexity constraint. Considering the problem of minimizing $P+\varepsilon R$ among convex subsets of $\mathbb{R}^N$ of fixed volume, where $P$…
Static spherically-symmetric matter distributions whose energy-momentum tensor is characterized by a non-negative trace are studied analytically within the framework of general relativity. We prove that such field configurations are…
This paper aims to explore a class of static stellar equilibrium configuration of relativistic charged spheres made of a charged perfect fluid. Solving the Einstein-Maxwell field equations, we consider a particularized metric potential,…
By applying the concepts of copositivity and using the gauge orbit spaces on the scalar potential, we derive analytic necessary and sufficient conditions which guarantee the boundedness of the scalar potential in all the directions in the…
In this paper, we prove the existence of minimizers of a class of multi-constrained variational problems. We consider systems involving a nonlinearity that does not satisfy compactness, monotonicity, neither symmetry properties. Our…
This paper investigates instances of Sobolev embeddings characterized by local compactness at every point within their domain, except for a single point. We obtain the sharp conditions that distinguish compactness from non-compactness and…
Attention has been recently called upon the fact that the weak and null energy conditions and the second law of thermodynamics are violated in wormhole solutions of Einstein's theory with classical, nonminimally coupled, scalar fields as…
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…
The Hodge equations for 1-forms are studied on Beltrami's projective disc model for hyperbolic space. Ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments. An existence theorem for…
A procedure for solving the Maxwell equations in vacuum, under the additional requirement that both scalar invariants are equal to zero, is presented. Such a field is usually called a null electromagnetic field. Based on the complex Euler…