Related papers: Energy quantization for biharmonic maps

In this paper is proposed a geometric solution to the dark energy, assuming that the space can be divided into regions of size $\sim L_{p}$ and energy $\sim E_{p}$. Significantly this assumption generate a energy density similar to the…

The set of world lines for the non-relativistic quartic oscillator satisfying Newton's equation of motion for all space and time in 1-1 dimensions with no constraints other than the "spring" restoring force is shown to be equivalent…

We review and compare different computational variational methods applied to a system of fourth order equations that arises as a model of cylinder buckling. We describe both the discretization and implementation, in particular how to deal…

We solve the weighted energy problem on the unit circle, by finding the extremal measure and describing its support. Applications to polynomial and exponential weights are also included.

We consider the equivariant wave maps equation $\mathbb{R}^{1+2} \to \mathbb{S}^2$, in all equivariance classes $k \in \mathbb{N}$. We prove that every finite energy solution resolves, continuously in time, into a superposition of…

Motivated by the theory of harmonic maps on Riemannian surfaces, conformal-harmonic maps between two Riemannian manifolds $M$ and $N$ were introduced in search of a natural notion of harmonicity for maps defined on a general even…

In a recent paper the first and the third authors introduced the notion of horizontal \alpha-harmonic map, with respect to a given C^1 planes distribution P_T on all R^m. The goal of this paper is to investigate compactness and quantization…

We develop a new approach to the invertibility of the layer potentials on $L^p$ associated with elliptic equations and systems in Lipschitz domains. As a consequence, for $n\ge 4$ and $(2(n-1)/(n+1))-\epsilon<p<2$, we obtain the solvability…

In the case of a large class of static spherically symmetric black hole solutions in higher order modified gravity models, an expression for the associated energy is proposed and identified as a quantity proportional to the constant of…

We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocusing case, we prove that arbitrary initial data in the energy space lead to global solutions that…

An ODE variational calculation shows that an image principle curvature ratio factor can raise the lower bound, 2(Image Area), on energy of a harmonic map of a surface into Rn. In certain situations, including all radially symmetry harmonic…

In this paper we show the energy identity and the no-neck property for $\varepsilon$- and $\alpha$-harmonic maps with homogeneous target manifolds. To prove this in the $\varepsilon$-harmonic case we introduce the idea of using an…

Dynamical energy analysis was recently introduced as a new method for determining the distribution of mechanical and acoustic wave energy in complex built up structures. The technique interpolates between standard statistical energy…

We calculate one-loop quantum energies in a renormalizable self-interacting theory in one spatial dimension by summing the zero-point energies of small oscillations around a classical field configuration, which need not be a solution of the…

In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…

A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic…

We present effective methods to compute equivariant harmonic maps from the universal cover of a surface into a nonpositively curved space. By discretizing the theory appropriately, we show that the energy functional is strongly convex and…

The quantization of the energy in a magnetic field (Landau quantization) at a three-quarter Dirac point is studied theoretically. The three-quarter Dirac point is realized in the system of massless Dirac fermions with the critically tilted…

We investigate the entanglement structure of a bipartite quantum system through the lens of quantum thermodynamics in the absence of conformal symmetry. Specifically, we consider the long-range Kitaev model, where the pairing interaction…

In a recent paper by Iglesias, Rumpf and Scherzer (Found. Comput. Math. 18(4), 2018) a variational model for deformations matching a pair of shapes given as level set functions was proposed. Its main feature is the presence of anisotropic…