**AMS/IP Studies in Advanced Mathematics**

Volume: 16;
2000;
461 pp;
Softcover

MSC: Primary 34; 35;

Print ISBN: 978-0-8218-2157-2

Product Code: AMSIP/16

List Price: $72.00

AMS Member Price: $57.60

MAA Member Price: $64.80

**Electronic ISBN: 978-1-4704-3807-4
Product Code: AMSIP/16.E**

List Price: $72.00

AMS Member Price: $57.60

MAA Member Price: $64.80

# Differential Equations and Mathematical Physics

Share this page *Edited by *
*Rudi Weikard; Gilbert Weinstein*

A co-publication of the AMS and International Press of Boston

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.

Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

#### Readership

Researchers and graduate students interested in differential equations and mathematical physics.

# Table of Contents

## Differential Equations and Mathematical Physics

- Cover Cover11
- Title page v6
- Contents vii8
- Preface xi12
- List of plenary speakers xiii14
- List of special sessions xv16
- List of participants and speakers xvii18
- On the Brown-Ravenhall relativistic Hamiltonian and the stability of matter 130
- Assessing accuracy in a numerical Einstein solver 1140
- Variational principle for the limit cycle of Rayleigh’s equation 2150
- Approach to the singularity in spatially inhomogeneous cosmologies 2756
- On the absolute continuity of the periodic Schrödinger and Dirac operators with magnetic potential 4170
- Correlations, spectral gap and log-Sobolev inequalities for unbounded spins systems 5180
- One dimensional regularizations of the Coulomb potential with application to atoms in strong magnetic fields 6796
- Construction of a solution to the semilinear elliptic equation in Chern-Simons gauge theory 77106
- Approximate eigenvectors and spectral theory 85114
- The initial value problem in the large and spacetime singularities 97126
- On the kernel of 𝑆𝑝𝑖𝑛^{𝑐} Dirac operators on 𝕊³ and ℝ³ 111140
- Realizing holonomic constraints in classical and quantum mechanics 121150
- A combined sine-Gordon and modified Korteweg-de Vries hierarchy and its algebro-geometric solutions 133162
- A minimax principle for eigenvalues in spectral gaps 175204
- Semiclassical dynamics and exponential asymptotics 181210
- Genericity of the band-gap structure of periodic media in the large coupling limit 197226
- Distribution of eigenvalues in the dense point spectrum of Schrödinger operators 207236
- On the distribution of scattering resonances for asymptotically hyperbolic manifolds 217246
- The multiformity of Lifshits tails caused by random Landau Hamiltonians with repulsive impurity potentials of different decay at infinity 233262
- Schrödinger operator perturbed by dynamics of lower dimension 249278
- Hyperbolic inverse problem with data on a part of the boundary 259288
- Best Sobolev inequalities on Riemannian manifolds 273302
- Self-energy of electrons in non-perturbative QED 279308
- The ground state energy of a dilute Bose gas 295324
- Trace formulae and completely integrable Hamiltonians 307336
- On the maximum and anti-maximum principles 323352
- The null condition and global existence of nonlinear elastic waves 339368
- The Hartree-Fock approximation in quantum electrodynamics–Positivity of the energy 347376
- Shock-wave cosmology 351380
- On some reverse inequalities in the Segal-Bargmann space 361390
- On the initial value problem of the Toda and Kac-van Moerbeke hierarchies 375404
- A class of non-selfadjoint Hill’s operators with analytic potentials 385414
- Regularized long wave-KP models 393422
- Spectral issues for block operator matrices 407436
- Some fully nonlinear equations in conformal geometry 425454
- 𝐿^{𝑝}-𝐿^{𝑝} estimates for the Schrödinger equation and inverse scattering 435464
- Stationary states of Vlasov system 449478
- Back Cover Back Cover1491