Regularity of solutions of divergence form elliptic equations

The aim of this paper is to study local regularity in the Morrey spaces of the first derivatives of the solutions of an elliptic second order equation in divergence form

where is assumed to be in some spaces and the coefficients belong to the space

     

The center of trace in spinning particles in General Relativity

The center of traceX _CT ⁱ of the energy-momentum tensor of a spinning particle in General Relativity is defined. It is shown to be an invariant point of the particle, and its path is shown to be what is specified by the original side condition of Mathisson,S u =0.     

Postulation of subschemes of irreducible curves on a quadric surface

We study all the possible Hilbert functions of 0-dimensional subschemes of irreducible curves of a smooth quadric of ℙ³. We obtain characterizations in case of complete intersection, arithmetically Cohen-Macaulay and arithmetically Buchsbaum curves and other necessary conditions in the general cases.     

Standard and goal-oriented adaptive mesh refinement applied to radiation transport on 2D unstructured triangular meshes

Standard and goal-oriented adaptive mesh refinement (AMR) techniques are presented for the linear Boltzmann transport equation. A posteriori error estimates are employed to drive the AMR process and are based on angular-moment information rather than on directional information, leading to direction-independent adapted meshes. An error estimate based on a two-mesh approach and a jump-based error indicator are compared for various test problems. In addition to the standard AMR approach, where the global error in the solution is diminished, a goal-oriented AMR procedure is devised and aims at reducing the error in user-specified quantities of interest. The quantities of interest are functionals of the solution and may include, for instance, point-wise flux values or average reaction rates in a subdomain. A high-order (up to order 4) Discontinuous Galerkin technique with standard upwinding is employed for the spatial discretization; the discrete ordinates method is used to treat the angular variable.     

On the regularity criteria for the 3D magnetohydrodynamic equations via two components in terms of BMO space

In this paper, we consider sufficient conditions for the regularity of Leray–Hopf solutions of the 3D incompressible magnetohydrodynamic equations via two components of the velocity and magnetic fields in terms of BMO spaces. We prove that if belongs to the space , then the solution (u,b) is regular. This extends recent results contained by Gala, Ji E and Lee J. Copyright © 2013 John Wiley & Sons, Ltd.     

Gravitation with a modified Weber force

With a modified Weber force for gravitation we show how the values of both the advance of the perihelion of the planets and the gravitational deflection of fast particles of general relativity can be reproduced.     

A Potential Theoretic Inequality

In this paper is proved a weighted inequality for Riesz potential similar to the classical one by D. Adams. Here the gain of integrability is not always algebraic, as in the classical case, but depends on the growth properties of a certain function measuring some local potential of the weight.