Related papers: Weighted energy problem on the unit circle
We prove a weighted a priori energy estimate for the two dimensional water-waves problem with contact points in the absence of gravity and surface tension. When the surface graph function and its time derivative have some decay near the…
A method for solving few-body scattering equations is proposed and examined. The solution of the scattering equations at complex energies is analytically continued to get scattering T-matrix with real positive energy. Numerical examples…
Some models are presented in which the strength of the gravitational coupling of the potential energy relative to the same coupling for the kinetic energy is, in a precise sense, adjustable. The gauge symmetry of these models consists of…
We deal with a weighted biharmonic problem in the unit ball of $\mathbb{R}^{4}$. The non-linearity is assumed to have critical exponential growth in view of Adam's type inequalities. The weight $w(x)$ is of logarithm type and the potential…
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…
The Equation Problem in finitely presented groups asks if there exists an algorithm which determines in finite amount of time whether any given equation system has a solution or not. We show that the Equation Problem in central extensions…
We consider the wave equation with a damping term on a partially rectangular planar domain, assuming that the damping is concentrated close to the non-rectangular part of the domain. Polynomial decay estimates for the energy of the solution…
Examination of symmetry energy is carried out on the basis of an elementary binding-energy formula. Constraints are obtained on the energy value at the normal nuclear density and on the density dependence of the energy at subnormal…
We study boundary value problems for degenerate elliptic equations and systems with square integrable boundary data. We can allow for degeneracies in the form of an $A_{2}$ weight. We obtain representations and boundary traces for solutions…
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…
In this article the solution of the special problem of the conditional extremum for the conjugate trigonometric polynomials is given. A possibility to apply this result to the problems of optimal stabilization of quasidynamic chaos in…
The aim of this chapter is to present an introduction and also an overview of some of the most relevant results concerning positivity energy theorems in General Relativity. These theorems provide the answer to a long standing problem that…
We revisit the negative energy solutions of the Dirac equation, which become relevant at very high energies and study several symmetries which follow therefrom. The consequences are briefly examined.
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
A new proof is given of the existence of the solution to electromagnetic (EM) wave scattering problem for an impedance body of an arbitrary shape. The proof is based on the elliptic systems theory and elliptic estimates for the solutions of…
We search for approximate, but analytic solutions of the pairing problem for one pair of nucleons in many levels of a potential well. For the collective energy a general formula, independent of the details of the single particle spectrum,…
We study the Euler equations with the so-called Ekman damping in the whole 2D space. The global well-posedness and dissipativity for the weak infinite energy solutions of this problem in the uniformly local spaces is verified based on the…
This paper is devoted to study the energy problem in general relativity using approximate Lie symmetry methods for differential equations. We evaluate second-order approximate symmetries of the geodesic equations for the stringy charged…
We use the so called resolvent transform method to study the cyclicity of the one point mass singular inner function in weighted Bergman type spaces.
We consider a singularly perturbed semilinear boundary value problem of a general form that allows various types of turning points. A solution decomposition is derived that separates the potential exponential boundary layer terms. The…