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Partial Differential Equations and Their Applications
Edited by: Peter C. Greiner, Victor Ivrii, Luis A. Seco, and Catherine Sulem, University of Toronto, ON, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques.

CRM Proceedings & Lecture Notes
1997; 315 pp; softcover
Volume: 12
ISBN-10: 0-8218-0687-4
ISBN-13: 978-0-8218-0687-6
List Price: US$105
Member Price: US$84
Order Code: CRMP/12
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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.


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


"The results presented and the variety of topics are impressive."

-- Monatshefte für Mathematik

Table of Contents

  • R. Beals, B. Gaveau, and P. Greiner -- Subelliptic geometry and fundamental solutions
  • M. Sh. Birman and A. Laptev -- "Non-standard" spectral asymptotics for a two-dimensional Schrödinger operator
  • R. E. Caflisch, N. Ercolani, and G. Steele -- Generic singularities for the steady Boussinesq equations
  • S.-Y. A. Chang -- On zeta functional determinant
  • P. Constantin -- Some mathematical aspects of incompressible fluid mechanics
  • W. Craig -- On the microlocal regularity of the Schrödinger kernel
  • G. Eskin and J. Ralston -- Inverse scattering problems for the Schrödinger operators with external Yang-Mills potentials
  • M. J. Esteban and E. Séré -- Existence and multiplicity of solutions for linear and nonlinear Dirac problems
  • C. L. Fefferman -- Stability of matter with magnetic fields
  • N. Ghoussoub -- A note on the multiplicity of surfaces with prescribed constant mean curvature
  • P. Guan and E. Sawyer -- The oblique derivative problem
  • S. Gustafson -- Stability of vortex solutions of the Ginzburg-Landau heat equation
  • M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, and N. Nadirashvili -- On some properties of zero sets and critical sets of solutions to elliptic equations
  • A. Laptev and Y. Safarov -- Szegő type theorems
  • V. Malkin -- Singularity formation for nonlinear Schrödinger equation and self-focusing of laser beams
  • Y. N. Ovchinnikov and I. M. Sigal -- Ginzburg-Landau equation I. Static vortices
  • J. C. Pipher -- Littlewood-Paley estimates: Some applications to elliptic boundary value problems
  • R. M. Pyke and I. M. Sigal -- Positive commutator methods for nonlinear wave equations. Constraints on periods and exponential decay of periodic solutions
  • D. Robert and V. Sordoni -- Generalized determinants for Sturm-Liouville problems on the real line
  • P. Sarnak -- Spectra and eigenfunctions of laplacians
  • A. Soffer and M. I. Weinstein -- Time dependent resonance theory and perturbations of embedded eigenvalues
  • M. Solomyak -- On the negative discrete spectrum of the operator \(-\Delta_{\mathcal{N}} - {\alpha}V\) for a class of unbounded domains in \(\mathbb{R}^d\)
  • P.-L. Sulem -- Vorticity structures in homogeneous turbulence
  • G. Zhislin -- Essential spectrum and \(SO(2)\)-symmetry of the energy operators of the 1uantum systems with nonincreasing magnetic field
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