相关论文: On the vector solutions of Maxwell equations with …

This paper considers a class of nonlinear time harmonic Maxwell systems at fixed frequency, with nonlinear terms taking the form $\mathscr{X}(x,|\vec E(x)|^2)\vec E(x)$, $\mathscr{Y}(x,|\vec H(x)|^2)\vec H(x)$, such that $\mathscr{X}(x,s)$,…

We present a systematic study of spherically symmetric vacuum solutions of the IKKT matrix model, within the framework of semi-classical covariant quantum geometries. All asymptotically flat solutions of the equations of motion of the frame…

The multidimensional gravity on the principal bundle with the SU(2) gauge group is considered. The numerical investigation of the spherically symmetric metrics with the center of symmetry is made. The solution of the gravitational equations…

Global stability of the spherically symmetric nonisentropic compressible Euler equations with positive density around global-in-time background affine solutions is shown in the presence of free vacuum boundaries. Vacuum is achieved despite…

Motivated by the observation of a recent renewal of rather strong interest in the description of bound states by (semi-) relativistic equations of motion, we revisit, for the example of the Woods-Saxon interactions, the eigenvalue problem…

The connection between spherical harmonics and symmetric tensors is explored. For each spherical harmonic, a corresponding traceless symmetric tensor is constructed. These tensors are then extended to include nonzero traces, providing an…

We define an abstract nonlinear elliptic system, admitting a variational structure, and including the vortex equations for some Maxwell-Chern-Simons gauge theories as special cases. We analyze the asymptotic behavior of its solutions, and…

In this paper we present some new results regarding the solvability of nonlinear Hammerstein integral equations in a special cone of continuous functions. The proofs are based on a certain fixed point theorem of Leggett and Williams type.…

We have derived the Wigner equations at global equilibrium with constant vorticity but space-time dependent electromagnetic fields up to second order in semiclassical expansion. We obtain the new second-order contributions to the charge…

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…

The magnetic field outside the earth is in good approximation a harmonic vector field determined by its values at the earth's surface. The direction problem seeks to determine harmonic vector fields vanishing at infinity and with prescribed…

By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some…

We consider solutions of some nonlinear parabolic boundary value problems in radial bounded domains whose initial profile satisfy a reflection inequality with respect to a hyperplane containing the origin. We show that, under rather general…

We present a new set of asymptotic conditions for gravity at spatial infinity that includes gravitational magnetic-type solutions, allows for a non-trivial Hamiltonian action of the complete $BMS_4$ algebra, and leads to a non-divergent…

The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…

Analytical solutions to the wave equation in spheroidal coordinates in the short wavelength limit are considered. The asymptotic solutions for the radial function are significantly simplified, allowing scalar spheroidal wave functions to be…

We consider two inverse boundary value problems for the time-harmonic Maxwell equations in an infinite slab. Assuming that tangential boundary data for the electric and magnetic fields at a fixed frequency is available either on subsets of…

The static black hole solutions to the Einstein-Maxwell equations are all spherically symmetric, as are many of the recently discovered black hole solutions in theories of gravity coupled to other forms of matter. However, counterexamples…

Symmetries of variational problems are considered as symmetries of vector bundle valued exterior differential systems. This approach is then applied to third order ordinary variational equations of motion of the semi-classical spinning…

We present a comprehensive construction of scalar, vector and tensor harmonics on maximally symmetric three-dimensional spaces. Our formalism relies on the introduction of spin-weighted spherical harmonics and a generalized helicity basis…