Partial Differential Equations and Mathematical Physics: In Memory of Jean Leray

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The 17 invited research articles in this volume, all written by leading experts in their respective fields, are dedicated to the French mathematician Jean Leray. A wide range of topics with significant new results - detailed proofs - are presented in the areas of partial differential equations, complex analysis and mathematical physics. Key subjects are: treated from the mathematical physics viewpoint - non-linear stability of an expanding universe, the compressible Euler equation, spin groups and the Leray-Maslov index; linked to the Cauchy problem - an intermediate case between effective hyperbolicity and the Levi condition, global Cauchy-Kowalewski theorem in some Gevrey classes, the analytic continuation of the solution, necessary conditions for hyperbolic systems, well posedness in the Gevrey class, uniformly diagonalizable systems and reduced dimension, and monodromy of ramified Cauchy problem. Addition articles examine results on: local solvability for a system of partial differential operators; the hypoellipticity of second order operators; differential forms and Hodge theory on analytic spaces; and sub elliptic operators and subriemanian geometry.