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# Differential Equations and Mathematical Physics

### About this Title

**Rudi Weikard**, *University of Alabama, Birmingham, Birmingham, AL* and **Gilbert Weinstein**, *University of Alabama, Birmingham, Birmingham, AL*, Editors

Publication: AMS/IP Studies in Advanced Mathematics

Publication Year:
2000; Volume 16

ISBNs: 978-0-8218-2157-2 (print); 978-1-4704-3807-4 (online)

DOI: https://doi.org/10.1090/amsip/016

MathSciNet review: MR1759613

MSC: Primary 00B25

### Table of Contents

**Front/Back Matter**

**Chapters**

- On the Brown-Ravenhall relativistic Hamiltonian and the stability of matter
- Assessing accuracy in a numerical Einstein solver
- Variational principle for the limit cycle of Rayleigh’s equation
- Approach to the singularity in spatially inhomogeneous cosmologies
- On the absolute continuity of the periodic Schrödinger and Dirac operators with magnetic potential
- Correlations, spectral gap and log-Sobolev inequalities for unbounded spins systems
- One dimensional regularizations of the Coulomb potential with application to atoms in strong magnetic fields
- Construction of a solution to the semilinear elliptic equation in Chern-Simons gauge theory
- Approximate eigenvectors and spectral theory
- The initial value problem in the large and spacetime singularities
- On the kernel of $Spin^c$ Dirac operators on $\mathbb S^3$ and $\mathbb {R}^3$
- Realizing holonomic constraints in classical and quantum mechanics
- A combined sine-Gordon and modified Korteweg-de Vries hierarchy and its algebro-geometric solutions
- A minimax principle for eigenvalues in spectral gaps
- Semiclassical dynamics and exponential asymptotics
- Genericity of the band-gap structure of periodic media in the large coupling limit
- Distribution of eigenvalues in the dense point spectrum of Schrödinger operators
- On the distribution of scattering resonances for asymptotically hyperbolic manifolds
- The multiformity of Lifshits tails caused by random Landau Hamiltonians with repulsive impurity potentials of different decay at infinity
- Schrödinger operator perturbed by dynamics of lower dimension
- Hyperbolic inverse problem with data on a part of the boundary
- Best Sobolev inequalities on Riemannian manifolds
- Self-energy of electrons in non-perturbative QED
- The ground state energy of a dilute Bose gas
- Trace formulae and completely integrable Hamiltonians
- On the maximum and anti-maximum principles
- The null condition and global existence of nonlinear elastic waves
- The Hartree-Fock approximation in quantum electrodynamics–Positivity of the energy
- Shock-wave cosmology
- On some reverse inequalities in the Segal-Bargmann space
- On the initial value problem of the Toda and Kac-van Moerbeke hierarchies
- A class of non-selfadjoint Hill’s operators with analytic potentials
- Regularized long wave-KP models
- Spectral issues for block operator matrices
- Some fully nonlinear equations in conformal geometry
- $L^p - L^{\acute {p}}$ estimates for the Schrödinger equation and inverse scattering
- Stationary states of Vlasov system