**CRM Proceedings & Lecture Notes**

Volume: 12;
1997;
315 pp;
Softcover

MSC: Primary 35;

Print ISBN: 978-0-8218-0687-6

Product Code: CRMP/12

List Price: $105.00

AMS Member Price: $84.00

MAA Member Price: $94.50

**Electronic ISBN: 978-1-4704-3926-2
Product Code: CRMP/12.E**

List Price: $105.00

AMS Member Price: $84.00

MAA Member Price: $94.50

# Partial Differential Equations and Their Applications

Share this page *Edited by *
*Peter C. Greiner; Victor Ivrii; Luis A. Seco; Catherine Sulem*

A co-publication of the AMS and Centre de Recherches Mathématiques

This volume presents lectures given at the 1995 Annual Seminar of the Canadian
Mathematical Society on Partial Differential Equations and Their Applications
held at the University of Toronto in June 1995.

The conference consisted of a combination of minicourses, invited
presentations, and contributed talks. In this volume readers will find
contributions on a variety of topics related to PDE, such as
spectral asymptotics, harmonic analysis, differential operators in hyperbolic
manifolds, applications to geometry, mathematical physics, hydrodynamics, and
the interaction between theory and numerical methods in PDE.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

#### Readership

Graduate students, research mathematicians, physicists, and engineers interested in nonlinear PDE, spectral asymptotics, geometric analysis, and mathematical physics.

#### Reviews & Endorsements

The results presented and the variety of topics are impressive.

-- Monatshefte für Mathematik

# Table of Contents

## Partial Differential Equations and Their Applications

- Cover Cover11
- Title page v6
- Contents vii8
- Preface ix10
- Subelliptic geometry and fundamental solutions 112
- "Non-standard" spectral asymptotics for a two-dimensional Schrödinger operator 920
- Generic singularities for the steady Boussinesq equations 1728
- On zeta functional determinant 2536
- Some mathematical aspects of incompressible fluid mechanics 5162
- On the microlocal regularity of the Schrödinger kernel 7182
- Inverse scattering problems for the Schrödinger operators with external Yang-Mills potentials 91102
- Existence and multiplicity of solutions for linear and nonlinear Dirac problems 107118
- Stability of matter with magnetic fields 119130
- A note on the multiplicity of surfaces with prescribed constant mean curvature 135146
- The oblique derivative problem 145156
- Stability of vortex solutions of the Ginzburg-Landau heat equation 159170
- On some properties of zero sets and critical sets of solutions to elliptic equations 167178
- Szegö type theorems 177188
- Singularity formation for nonlinear Schrödinger equation and self-focusing of laser beams 183194
- Ginzburg-Landau equation I. Static vortices 199210
- Littlewood-Paley estimates: Some applications to elliptic boundary value problems 221232
- Positive commutator methods for nonlinear wave equations. Constraints on periods and exponential decay of periodic solutions 239250
- Generalized determinants for Sturm-Liouville problems on the real line 251262
- Spectra and eigenfunctions of laplacians 261272
- Time dependent resonance theory and perturbations of embedded eigenvalues 277288
- On the negative discrete spectrum of the operator -Δ_{𝒩}-𝛼𝒱 for a class of unbounded domains in ℝ^{𝕕} 283294
- Vorticity structures in homogeneous turbulence 297308
- Essential spectrum and 𝑆𝑂(2)-symmetry of the energy operators of the Quantum systems with nonincreasing magnetic field 307318
- Back Cover Back Cover1327