Related papers: Weighted energy problem on the unit circle
We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases one can "hear" the weights of a weighted projective space.
In this paper, we use probabilistic approach to prove that there exists a unique weak solution to the Dirichlet boundary value problem for second order elliptic equations whose coefficients are signed measures, and we will give a…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the…
In this paper, we investigate discrete logarithmic energy problems in the unit circle. We study the equilibrium configuration of $n$ electrons and $n-1$ pairs of external protons of charge $+1/2$. It is shown that all the critical points of…
We show convergence of minimizers of weighted inertia-energy functionals to solutions of initial value problems for a class of nonlinear wave equations. The result is given for the nonhomogeneous case under a natural growth assumption on…
The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtained by variational methods.
In this paper we study an optimal control problem associated to a linear degenerate elliptic equation with mixed boundary conditions. The equations of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions. We…
Solutions to the Einstein equation that represent the superposition of static isolated bodies with axially symmetry are presented. The equations nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies. The…
Energy problems are important in the formal analysis of embedded or autonomous systems. Using recent results on star-continuous Kleene omega-algebras, we show here that energy problems can be solved by algebraic manipulations on the…
We set up a model of an electric charge where the noninvertible metric phase of first order gravity supercedes the point charge singularity in a curved spacetime. A topological interpretation of the electric charge is provided in terms of…
We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.
The energy and momentum for different cosmological models using various prescriptions are evaluated. In particular, we have focused our attention on the energy and momentum for gravitational waves and discuss the results. It is concluded…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
We consider symmetric Dirichlet forms on locally compact and non-locally compact spaces and provide an elementary proof for their closability with respect to energy dominant measures. We also discuss how to use known potential theoretic…
Spherical means are well-known useful tool in the theory of partial differential equations with applications to solving hyperbolic and ultrahyperbolic equations and problems of integral geometry, tomography and Radon transforms. We…
We prove local energy decay for the damped wave equation on R^d. The problem which we consider is given by a long range metric perturbation of the Euclidean Laplacian with a short range absorption index. Under a geometric control assumption…
In this paper, we investigate the two-point boundary value problems for linear wave equation defined on a circle and prove that the equation possesses the exact controllability. We also investigate the two-point boundary value problems for…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part, according to variational approach we obtain a…
On a K\"ahler manifold we consider the problems of maximizing/minimizing Monge--Amp\`ere energy over certain subsets of the space of K\"ahler potentials. Under suitable assumptions we prove that solutions to these variational problems…