18 research outputs found
Improved Sobolev Embedding Theorems for Vector-valued Functions
The aim of this paper is to give an extension of the improved Sobolev
embedding theorem for single-valued functions to the case of vector-valued
functions which is involved with the three-dimensional massless Dirac operator
together with the three- or two-dimensional Weyl--Dirac (or Pauli) operator,
the Cauchy--Riemann operator and also the four-dimensional Euclidian Dirac
operator.Comment: 40 pages. To appear in Funkcialaj Ekvacioj 57 (2014
On the asymptotic behavior of the solutions of the Schrödinger equation (-⊿+Q(y)-k²)V=F
The principle of limiting absorption for the non-selfadjoint Schrödinger operator in R²
Spectral and scattering theory for second-order differential operators with operator-valued coefficients
Eigenfunction expansions for the Schrödinger operators with long-range potentials Q(y)=O(|y|^-ε), ε>0
The asymptotic limits of zero modes of massless Dirac operators
Asymptotic behaviors of zero modes of the massless Dirac operator
are discussed, where
is the triple of Dirac
matrices, , and is a
Hermitian matrix-valued function with
, .
We shall show that for every zero mode , the asymptotic limit of
as exists. The limit is expressed in terms of an
integral of .Comment: 9 page
Eigenfunctions at the threshold energies of magnetic Dirac operators
Discussed are modes and resonances of Dirac operators with
vector potentials . Asymptotic
limits of modes at infinity are derived when ,
, provided that has modes. In wider classes of vector
potentials, sparseness of the vector potentials which give rise to the
modes of are established. It is proved that no has
resonances if , .Comment: 25 pages, New results are adde
International Conference on Differential Equations and Mathematical Physics
The meeting in Birmingham, Alabama, provided a forum for the discussion of recent developments in the theory of ordinary and partial differential equations, both linear and non-linear, with particular reference to work relating to the equations of mathematical physics. The meeting was attended by about 250 mathematicians from 22 countries. The papers in this volume all involve new research material, with at least outline proofs; some papers also contain survey material. Topics covered include: Schrödinger theory, scattering and inverse scattering, fluid mechanics (including conservative systems and inertial manifold theory attractors), elasticity, non-linear waves, and feedback control theory