Partial Differential Equations and Mathematical Physics

The 17 invited research articles in this volume, all written by
leading experts in their respective fields, are dedicated to the great
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: nonlinear 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.
Additional 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, * Subelliptic operators and sub-
Riemannian geometry.
Contributors: V. Ancona, R. Beals, A. Bove, R. Camales, Y. Choquet-
Bruhat, F. Colombini, M. De Gosson, S. De Gosson, M. Di Flaviano, B.
Gaveau, D. Gourdin, P. Greiner, Y. Hamada, K. Kajitani, M. Mechab, K.
Mizohata, V. Moncrief, N. Nakazawa, T. Nishitani, Y. Ohya, T. Okaji,
S. Ouchi, S. Spagnolo, J. Vaillant, C. Wagschal, S. Wakabayashi
The book is suitable as a reference text for graduate students and
active researchers.