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

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.

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Content:
Front Matter....Pages i-xi
Differential Forms, Cycles and Hodge Theory on Complex Analytic Spaces....Pages 1-11
On Exact Solutions of Linear PDEs....Pages 13-29
Necessary Conditions for Hyperbolic Systems....Pages 31-49
Monodromy of the Ramified Cauchy Problem....Pages 51-56
Nonlinear Stability of an Expanding Universe with the S 1 Isometry Group....Pages 57-71
On the Cauchy Problem for a Weakly Hyperbolic Operator: An Intermediate Case Between Effective Hyperbolicity and Levi Condition....Pages 73-83
Symplectic Path Intersections and the Leray Index....Pages 85-96
A Global Cauchy—Kowalewski Theorem in Some Gevrey Classes....Pages 97-104
Sub-Riemannian Geometry and Subelliptic PDEs....Pages 105-110
On the Analytic Continuation of the Solution of the Cauchy Problem....Pages 111-119
Strong Gevrey Solvability for a System of Linear Partial Differential Equations....Pages 121-141
Spherically Symmetric Solutions of the Compressible Euler Equation....Pages 143-150
Hyperbolic Cauchy Problem Well Posed in the Class of Gevrey....Pages 151-156
Absence of Eigenvalues of Dirac Type Operators....Pages 157-176
The Behaviors of Singular Solutions of Partial Differential Equations in Some Class in the Complex Domain....Pages 177-194
Syst?mes Uniform?ment Diagonalisables, Dimension R?duite et Sym?trie II....Pages 195-223
On Hypoellipticity of the Operator $ exp left[ { - {{left| {{x_1}} right|}^{ - sigma }}} right]D_1^2 + x_1^4D_2^2 + 1$ ....Pages 225-238
Back Matter....Pages 239-243

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Content:
Front Matter....Pages i-xi
Differential Forms, Cycles and Hodge Theory on Complex Analytic Spaces....Pages 1-11
On Exact Solutions of Linear PDEs....Pages 13-29
Necessary Conditions for Hyperbolic Systems....Pages 31-49
Monodromy of the Ramified Cauchy Problem....Pages 51-56
Nonlinear Stability of an Expanding Universe with the S 1 Isometry Group....Pages 57-71
On the Cauchy Problem for a Weakly Hyperbolic Operator: An Intermediate Case Between Effective Hyperbolicity and Levi Condition....Pages 73-83
Symplectic Path Intersections and the Leray Index....Pages 85-96
A Global Cauchy—Kowalewski Theorem in Some Gevrey Classes....Pages 97-104
Sub-Riemannian Geometry and Subelliptic PDEs....Pages 105-110
On the Analytic Continuation of the Solution of the Cauchy Problem....Pages 111-119
Strong Gevrey Solvability for a System of Linear Partial Differential Equations....Pages 121-141
Spherically Symmetric Solutions of the Compressible Euler Equation....Pages 143-150
Hyperbolic Cauchy Problem Well Posed in the Class of Gevrey....Pages 151-156
Absence of Eigenvalues of Dirac Type Operators....Pages 157-176
The Behaviors of Singular Solutions of Partial Differential Equations in Some Class in the Complex Domain....Pages 177-194
Syst?mes Uniform?ment Diagonalisables, Dimension R?duite et Sym?trie II....Pages 195-223
On Hypoellipticity of the Operator $ exp left[ { - {{left| {{x_1}} right|}^{ - sigma }}} right]D_1^2 + x_1^4D_2^2 + 1$ ....Pages 225-238
Back Matter....Pages 239-243
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