On the diffraction of high-frequency waves by arbitrary shape cone. Neumann case
On the exterior magnetic field and silent sources in magnetoencephalography.
On the geometry of convex reflectors
In this paper we consider a special class of convex hypersurfaces in Euclidean space which arise as weak solutions to some inverse problems of recovering reflectors from scattering data. For this class of hypersurfaces we study the notion of the focal function which, while sharing the important convexity property with the classical support function, has the advantage of being exactly the "right tool" for such inverse problems. We also discuss briefly the close analogy between one such inverse problem...
On the Ginzburg-Landau and related equations
We describe qualitative behaviour of solutions of the Gross-Pitaevskii equation in 2D in terms of motion of vortices and radiation. To this end we introduce the notion of the intervortex energy. We develop a rather general adiabatic theory of motion of well separated vortices and present the method of effective action which gives a fairly straightforward justification of this theory. Finally we mention briefly two special situations where we are able to obtain rather detailed picture of the vortex...
On the linear force-free fields in bounded and unbounded three-dimensional domains
On the linear force-free fields in bounded and unbounded three-dimensional domains
Linear Force-free (or Beltrami) fields are three-components divergence-free fields solutions of the equation curlB = αB, where α is a real number. Such fields appear in many branches of physics like astrophysics, fluid mechanics, electromagnetics and plasma physics. In this paper, we deal with some related boundary value problems in multiply-connected bounded domains, in half-cylindrical domains and in exterior domains.
On the low frequency asymptotics in electromagnetic theory.
On the mathematical basis of the linear sampling method.
On the Mathematics of EEG and MEG in Spheroidal Geometry
On the Maxwell's system in composite media
On the method of successive approximations for the J. L. Synge electromagnetic two-body problem.
On the point limit of the Pauli-Fierz model
On the positioning problem of a microscopic particle trapped in optical tweezers.
On the profiles of nonlinear geometric optics
On the propagation of surface electromagnetic waves analogous to Rayleigh waves in the case of Leontovich boundary conditions.
On the Relation between the S-matrix and the Spectrum of the Interior Laplacian
The main results of this paper are: 1) a proof that a necessary condition for 1 to be an eigenvalue of the S-matrix is real analyticity of the boundary of the obstacle, 2) a short proof that if 1 is an eigenvalue of the S-matrix, then k² is an eigenvalue of the Laplacian of the interior problem, and that in this case there exists a solution to the interior Dirichlet problem for the Laplacian, which admits an analytic continuation to the whole space ℝ³ as an entire function.
On the singular values and eigenvalues of the Fox-Li and related operators.
On the spectrum of the reduced wave operators with cylindrical discontinuity.
On the strong unique continuation prinicple for inequalities of Maxwell type.
On the support of the equilibrium measure for arcs of the unit circle and for real intervals.