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Recent work in the literature had evaluated the energy-momentum tensor of a Casimir apparatus in a weak gravitational field, for an electromagnetic field subject to perfect conductor boundary conditions on parallel plates. The Casimir…
Compatibility conditions are investigated for planar network structures consisting of nodes and connecting bars; these conditions restrict the elongations of bars and are analogous to the compatibility conditions of deformation in continuum…
In this work, we explore a class of compact charged spheres that have been tested against experimental and observational constraints with some known compact stars candidates. The study is performed by considering the self-gravitating,…
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…
We consider a nonlinear Schr\"odinger equation with focusing nonlinearity of power type on a star graph ${\mathcal G}$, written as $ i \partial_t \Psi (t) = H \Psi (t) - |\Psi (t)|^{2\mu}\Psi (t)$, where $H$ is the selfadjoint operator…
Local versions of measurability have been around for a long time. Roughly, one splits the notion of $\mu $-completeness into pieces, and asks for a uniform ultrafilter over $\mu $ satisfying just some piece of $\mu $-completeness. Analogue…
This paper deals with singular/degenerate semilinear critical equations which arise as the Euler-Lagrange equation of Caffarelli-Kohn-Nirenberg inequalities in $\mathbb{R}^d$, with $d\geq 2$. We prove several rigidity results for positive…
We propose a new formalism to analyse the extremum structure of scale-invariant effective potentials. The problem is stated in a compact matrix form, used to derive general expressions for the stationary point equation and the mass matrix…
We consider four dimensional lie groups equipped with left invariant Lorentzian Einstein metrics, and determine the harmonicity properties of vector fields on these spaces. In some cases, all these vector fields are critical points for the…
In this work, we provide some novel results that establish both the existence of Henig global proper efficient points and their density in the efficient set for vector optimization problems in arbitrary normed spaces. Our results do not…
In this work we investigate the matrix elements of the energy-momentum tensor for massless on-shell states in four-dimensional unitary, local, and Poincar\'e covariant quantum field theories. We demonstrate that these matrix elements can be…
There has been much recent work on quantum inequalities to constrain negative energy. These are uncertainty principle-type restrictions on the magnitude and duration of negative energy densities or fluxes. We consider several examples of…
A key question in the analysis of discrete models for material defects, such as vortices in spin systems and superconductors or isolated dislocations in metals, is whether information on boundary energy for a domain can be sufficient for…
The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…
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…
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…
The latest cosmological constraints on the sum of the neutrino masses depend on prior physical assumptions about the mass spectrum. To test the accordance of cosmological and laboratory constraints in the absence of such priors, we…
A previous work found that a nonminimally coupled theory of gravity can, under appropriate conditions, give rise to an additional contribution to the field equations interpreted as dark matter [1]: in particular, the density of this dark…
We obtain localized field configurations with finite energy in a ($2+1$)-dimensional model with Maxwell and Chern-Simons gauge terms coupled to a massive complex scalar field. These non-topological solitons are characterized by the $U(1)$…
This paper is concerned with a study of the classical isoperimetric problem modified by an addition of a non-local repulsive term. We characterize existence, non-existence and radial symmetry of the minimizers as a function of mass in the…