Partial Differential Equations and Their Applications

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.

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