Partial Differential Equations and Mathematical Physics

On March 17-19 and May 19-21,1995, analysis seminars were organized jointly at the universities of Copenhagen and Lund, under the heading "Danish-Swedish Analysis Seminar". The main topic was partial differen tial equations and related problems of mathematical physics. The lectures given are presented in this volume, some as short abstracts and some as quite complete expositions or survey papers. They span over a large vari ety of topics. The most frequently occurring theme is the use of microlocal analysis which is now important also in the study of non-linear differential equations although it originated entirely within the linear theory. Perhaps it is less surprising that microlocal analysis has proved to be useful in the study of mathematical problems of classical quantum mechanics, for it re ceived a substantial input of ideas from that field. The scientific committee for the invitation of speakers consisted of Gerd Grubb in Copenhagen, Lars Hormander and Anders MeHn in Lund, and Jo hannes Sjostrand in Paris. Lars Hormander and Anders Melin have edited the proceedings. They were hosts of the seminar days in Lund while Gerd Grubb was the host in Copenhagen. Financial support was obtained from the mathematics departments in Copenhagen and Lund, CNRS in France, the Danish and Swedish Na tional Research Councils, Gustaf Sigurd Magnuson's foundation at the Royal Swedish Academy of Sciences, and the Wenner-Gren foundation in Stockholm. We want to thank all these organisations for their support.

Autorentext
Lars Hörmander, born 1931 in Sweden, did his secondary schooling as well as his undergraduate and doctoral studies in Lund. His principle teacher and adviser at the University of Lund was Marcel Riesz until he returned, then Lars Gårding. In 1956 he worked in the USA, at the universities of Chicago, Kansas, Minnesota and New York, before returning to a chair at the University of Stockholm. He remained a frequent visitor to the US, particularly to Stanford and was Professor at the IAS, Princeton from 1964 to 1968. In 1968 he accepted a chair at the University of Lund, Sweden, where, today, he is Emeritus Professor.

Hörmander's lifetime work has been devoted to the study of partial differential equations and its applications in complex analysis. In 1962 he was awarded the Fields Medal for his contributions to the general theory of linear partial differential operators.

Zusammenfassung
This volume presents lectures from the Danish-Swedish Analysis Seminar 1995, covering themes in mathematical physics, spanning a wide variety of topics.

Inhalt
On perturbation of embedded eigenvalues.- Blowup of classical solutions of nonlinear hyperbolic equations: a survey of recent results.- Global time decay of the amplitude of a reflected wave.- Weyl quantization and Fourier integral operators.- The local index theorem without smoothness.- How ideas from microlocal analysis can be applied in 2-D fluid mechanics.- Lp spectral independence for certain uniformly elliptic operators.- Trace asymptotics via almost analytic extensions.- A microlocal version of concentration-compactness.- Complete heat trace, resolvent and zeta expansions for general Atiyah-Patodi-Singer problems.- Semi-classical analysis for the transfer operator: WKB constructions in dimension 1.- Several recent results in nonlinear geometric optics.- Stabilization of the wave equation by the boundary.- About small-power semilinear wave equations.- The Faddeev approach to inverse scattering from a micro-local perspective.- Fibrations, compactifications and algebras of pseudodifferential operators.- Degree theory beyond continuous maps.- On the Weyl formula for obstacles.- On the asymptotic completeness for particles in constant electromagnetic fields.- The size of atoms in Hartree-Fock theory.- Holomorphic extension of CR functions: a survey.- Local solvability in a class of overdetermined systems of linear PDE.- Neumann resonances in linear elasticity.