A boundary value problem for the wave equation.
A characterization of balls using the domain derivative.
A class of generalized integral operators.
A class of --Laplacian type equation with potentials eigenvalue problem in .
A counterexample to the “hot spots" conjecture.
A criterion for discrete spectra of partial differential operators
A directional compactification of the complex Bloch variety.
A directional compactification of the complex Fermi surface and isospectrality
A discrete Hardy-Laptev-Weidl-type inequality and associated Schrödinger-type operators.
A discreteness criterion for the spectrum of the Laplace--Beltrami operator on quasimodel manifolds.
A double eigenvalue problem for Schrödinger equations involving sublinear nonlinearities at infinity.
A general perturbation formula for electromagnetic fields in presence of low volume scatterers
In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This...
A general perturbation formula for electromagnetic fields in presence of low volume scatterers
In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This...
A global bifurcation result of a Neumann problem with indefinite weight.
A global continuation theorem for obtaining eigenvalues and bifurcation points
A Hörmander-type spectral multiplier theorem for operators without heat kernel
Hörmander’s famous Fourier multiplier theorem ensures the -boundedness of whenever for some , where we denote by the set of functions satisfying the Hörmander condition for derivatives. Spectral multiplier theorems are extensions of this result to more general operators and yield the -boundedness of provided for some sufficiently large. The harmonic oscillator shows that in general is not sufficient even if has a heat kernel satisfying gaussian estimates. In this paper,...
A lower bound for the error term in Weyl’s law for certain Heisenberg manifolds, II
This article is concerned with estimations from below for the remainder term in Weyl’s law for the spectral counting function of certain rational (2ℓ + 1)-dimensional Heisenberg manifolds. Concentrating on the case of odd ℓ, it continues the work done in part I [21] which dealt with even ℓ.
A lower bound for the principal eigenvalue of the Stokes operator in a random domain
This article is dedicated to localization of the principal eigenvalue (PE) of the Stokes operator acting on solenoidal vector fields that vanish outside a large random domain modeling the pore space in a cubic block of porous material with disordered micro-structure. Its main result is an asymptotically deterministic lower bound for the PE of the sum of a low compressibility approximation to the Stokes operator and a small scaled random potential term, which is applied to produce a similar bound...
A maxmin principle for nonlinear eigenvalue problems with application to a rational spectral problem in fluid-solid vibration
In this paper we prove a maxmin principle for nonlinear nonoverdamped eigenvalue problems corresponding to the characterization of Courant, Fischer and Weyl for linear eigenproblems. We apply it to locate eigenvalues of a rational spectral problem in fluid-solid interaction.
A mean-value lemma and applications
We control the gap between the mean value of a function on a submanifold (or a point), and its mean value on any tube around the submanifold (in fact, we give the exact value of the second derivative of the gap). We apply this formula to obtain comparison theorems between eigenvalues of the Laplace-Beltrami operator, and then to compute the first three terms of the asymptotic time-expansion of a heat diffusion process on convex polyhedrons in euclidean spaces of arbitrary dimension. We also write...