Related papers: Minimum Energy Problem on the Hypersphere
We study the dependence of least nontrivial critical levels of the energy functional corresponding to the zero Dirichlet problem $-\Delta_p u = f(u)$ in a bounded domain $\Omega \subset \mathbb{R}^N$ upon domain perturbations. Assuming that…
The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several…
We present a theoretical study of the processes d(d,p)3H and d(d,n)3He at energies of interest for energy production and for big-bang nucleosynthesis. We accurately solve the four body scattering problem using the ab-initio hyperspherical…
The paper deals with minimum energy problems in the presence of external fields with respect to the Riesz kernels $|x-y|^{\alpha-n}$, $0<\alpha<n$, on $\mathbb R^n$, $n\geqslant2$. For quite a general (not necessarily lower semicontinuous)…
We study the general properties of fluid spheres satisfying the heuristic assumption that their areas and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all…
We develop an exact method for computing the Casimir energy between arbitrary compact objects, both with boundary conditions for a scalar field and dielectrics or perfect conductors for the electromagnetic field. The energy is obtained as…
A family of spin-lattice models are derived as convergent finite dimensional approximations to the rest frame kinetic energy of a barotropic fluid coupled to a massive rotating sphere. In not fixing the angular momentum of the fluid…
I develop the idea that our world is a brane-like object embedded in Euclidean bulk. In its ground state, the brane constituent matter is assumed to be homogeneous and isotropic, and of negligible influence on the bulk geometry. The…
Each non-zero point in $\mathbb{R}^d$ identifies a closest point $x$ on the unit sphere $\mathbb{S}^{d-1}$. We are interested in computing an $\epsilon$-approximation $y \in \mathbb{Q}^d$ for $x$, that is exactly on $\mathbb{S}^{d-1}$ and…
In a matter-filled spacetime, perhaps with positive cosmological constant, a stable marginally outer trapped 2-sphere must satisfy a certain area inequality. Namely, as discussed in the paper, its area must be bounded above by $4\pi/c$,…
We investigate the differentiability of minimal average energy associated to the functionals $S_\ep (u) = \int_{\mathbb{R}^d} (1/2)|\nabla u|^2 + \ep V(x,u)\, dx$, using numerical and perturbative methods. We use the Sobolev gradient…
To begin with, we identify the equations of elastostatics in a Riemannian manifold, which generalize those of classical elasticity in the three-dimensional Euclidean space. Our approach relies on the principle of least energy, which asserts…
We define the state of minimum energy while the expectation values of the field operators and their time derivatives in a determined moment in such a state are constrained. As an axiom, we consider such a state as the background of the…
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…
Densities of particles on $\Rn$ which interact pairwise through an attractive-repulsive power-law potential $W_{\al,\bt}(x) = |x|^\al/\al-|x|^\bt/\bt$ have often been used to explain patterns produced by biological and physical systems. In…
We study the following Lane-Emden system \[ -\Delta u=|v|^{q-1}v \quad \text{ in } \Omega, \qquad -\Delta v=|u|^{p-1}u \quad \text{ in } \Omega, \qquad u_\nu=v_\nu=0 \quad \text{ on } \partial \Omega, \] with $\Omega$ a bounded regular…
In this paper, we study additive properties of finite sets of lattice points on spheres in $3$ and $4$ dimensions. Thus, given $d,m \in \mathbb{N}$, let $A$ be a set of lattice points $(x_1, \dots, x_d) \in \mathbb{Z}^d$ satisfying $x_1^2 +…
The cosmological constant (vacuum energy) problem is analyzed within the scope of quantum theories with UV-cut-off or fundamental length. Various cases associated with the appearance of the latter are considered both using the Generalized…
We study the existence of positive solutions for the following class of scalar field problem on the hyperbolic space $$ -\Delta_{\mathbb{H}^N} u - \lambda u = a(x) |u|^{p-1} \, u\;\;\text{in}\;\mathbb{B}^{N}, \quad u \in…
We consider the problem of two interacting particles on a sphere. The potential of the interaction depends on the distance between the particles. The case of Newtonian-type potentials is studied in most detail. We reduce this system to a…