Differential Equations and Mathematical Physics

This volume contains the proceedings of the 1999 International Conference on Differential Equations and Mathematical Physics. The contributions selected for this volume represent some of the most important presentations by scholars from around the world on developments in this area of research. The papers cover topics in the general area of linear and nonlinear differential equations and their relation to mathematical physics, such as multiparticle Schrödinger operators, stability of matter, relativity theory, fluid dynamics, spectral and scattering theory including inverse problems.

• A. A. Balinsky and W. D. Evans -- On the Brown-Ravenhall relativistic Hamiltonian and the stability of matter
• R. Bartnik -- Assessing accuracy in a numerical Einstein solver
• R. D. Benguria and M. C. Depassier -- Variational principle for the limit cycle of Rayleigh's equation
• B. K. Berger -- Approach to the singularity in spatially inhomogeneous cosmologies
• M. Sh. Birman and T. A. Suslina -- On the absolute continuity of the periodic Schrödinger and Dirac operators with magnetic potential
• T. Bodineau and B. Helffer -- Correlations, spectral gap and log-Sobolev inequalities for unbounded spins systems
• R. Brummelhuis, M. B. Ruskai, and E. Werner -- One dimensional regularizations of the Coulomb potential with application to atoms in strong magnetic fields
• D. Chae and O. Yu. Imanuvilov -- Construction of a solution to the semilinear elliptic equation in Chern-Simons gauge theory
• M. Christ, A. Kiselev, and Y. Last -- Approximate eigenvectors and spectral theory
• D. Christodoulou -- The initial value problem in the large and spacetime singularities
• L. Erdös and J. P. Solovej -- On the kernel of $Spin^c$ Dirac operators on $\mathbb S^3$ and $\mathbb{R}^3$
• R. Froese and I. Herbst -- Realizing holonomic constraints in classical and quantum mechanics
• F. Gesztesy and H. Holden -- A combined sine-Gordon and modified Korteweg-de Vries hierarchy and its algebro-geometric solutions
• M. Griesemer -- A minimax principle for eigenvalues in spectral gaps
• G. A. Hagedorn and A. Joye -- Semiclassical dynamics and exponential asymptotics
• R. Hempel and K. Lienau -- Genericity of the band-gap structure of periodic media in the large coupling limit
• A. M. Hinz -- Distribution of eigenvalues in the dense point spectrum of Schrödinger operators
• P. D. Hislop -- On the distribution of scattering resonances for asymptotically hyperbolic manifolds
• T. Hupfer, H. Leschke, and S. Warzel -- The multiformity of Lifshits tails caused by random Landau Hamiltonians with repulsive impurity potentials of different decay at infinity
• W. Karwowski and V. Koshmanenko -- Schrödinger operator perturbed by dynamics of lower dimension
• Y. V. Kurylev and M. Lassas -- Hyperbolic inverse problem with data on a part of the boundary
• Y. Li -- Best Sobolev inequalities on Riemannian manifolds
• E. H. Lieb and M. Loss -- Self-energy of electrons in non-perturbative QED
• E. H. Lieb and J. Yngvason -- The ground state energy of a dilute Bose gas
• M. Ohmiya -- Trace formulae and completely integrable Hamiltonians
• Y. Pinchover -- On the maximum and anti-maximum principles
• T. C. Sideris -- The null condition and global existence of nonlinear elastic waves
• H. Siedentop -- The Hartree-Fock approximation in quantum electrodynamics-Positivity of the energy
• J. A. Smoller and J. B. Temple -- Shock-wave cosmology
• S. B. Sontz -- On some reverse inequalities in the Segal-Bargmann space
• G. Teschl -- On the initial value problem of the Toda and Kac-van Moerbeke hierarchies
• V. Tkachenko -- A class of non-selfadjoint Hill's operators with analytic potentials
• M. M. Tom -- Regularized long wave-KP models
• C. Tretter -- Spectral issues for block operator matrices
• J. A. Viaclovsky -- Some fully nonlinear equations in conformal geometry
• R. Estimates for the Schrödinger equation and inverse scattering
• G. Wolanski -- Stationary states of Vlasov system