相关论文: Maxwell meets Korn: A New Coercive Inequality for …
In this paper we look for solutions of a semilinear Maxwell type equation, in even dimension, greater than four. These solutions are critical points of a functional which is strongly degenerate because of the presence of the exterior…
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
We perform a detailed analysis of the solvability of linear strain equations on hyperbolic surfaces to obtain $L^2$ regularity solutions. Then the rigidity results on the strain tensor of the middle surface are implied by the $L^2$…
In this work we establish a density-functional reformulation of coupled matter-photon problems subject to general external electromagnetic fields and charge currents. We first show that for static minimally-coupled matter-photon systems an…
This paper deals with solutions of the divergence for domains with external cusps. It is known that the classic results in standard Sobolev spaces, which are basic in the variational analysis of the Stokes equations, are not valid for this…
In this paper the Maxwell field theory is considered on a closed and orientable Riemann surface of genus $h>1$. The solutions of the Maxwell equations corresponding to nontrivial values of the first Chern class are explicitly constructed…
We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.
A nonlinear Korn inequality based on the Green-Saint Venant strain tensor is proved, whenever the displacement is in the Sobolev space $W^{1,p}$, $p\geq 2$, under Dirichlet conditions on a part of the boundary. The inequality can be useful…
We develop a quantization scheme for Maxwell's equations without source on an arbitrary four dimensional globally hyperbolic spacetime. The field strength tensor is the key dynamical object and it is not assumed a priori that it descends…
We evaluate the quantum correlators associated with the Maxwell field vacuum distorted by the presence of plane parallel material surfaces. Regularization is performed through the generalized zeta funtion technique. Results are applied to a…
To simulate open boundaries within finite computation domain, real-function coordinate transformation in the framework of generally covariant formulation of Maxwell equations is proposed. The mapping--realized with arctangent function…
This paper aims to show that making use of Newton's view on equations of motion of a physical system and of the Maxwell stress tensor we come to a natural nonlinearization of Maxwell equations in vacuum making use only of nonrelativistic…
The basic concepts of exterior calculus for space-time multivectors are presented: interior and exterior products, interior and exterior derivatives, oriented integrals over hypersurfaces, circulation and flux of multivector fields. Two…
In this work we take into consideration a generalization of Gauge Theories based on the analysis of the structural characteristics of Maxwell theory, which can be considered as the prototype of such kind of theories (Maxwell-like). Such…
It is shown that there is a correspondence between field theory equations such as the Dirac, Shr\H{o}dinger, Maxwell, Einstein equations and closed exterior forms of a certain degree. In this case, the Dirac and Shr\H{o}dinger equations for…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
We show a weighted version of Korn inequality on bounded euclidean John domains, where the weights are nonnegative powers of the distance to the boundary. In this theorem, we also provide an estimate of the constant involved in the…
This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximated by means of a novel approach based on the splitting of the…