Partial Differential Equations IV

1. Front Matter

   Pages i-vii

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2. Microlocal Analysis

   • Yu. V. Egorov

   Pages 1-147

3. Linear Hyperbolic Equations

   • V. Ya. Ivrii

   Pages 149-235

4. Back Matter

   Pages 237-244

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In the first part of this EMS volume Yu.V. Egorov gives an account of microlocal analysis as a tool for investigating partial differential equations. This method has become increasingly important in the theory of Hamiltonian systems. Egorov discusses the evolution of singularities of a partial differential equation and covers topics like integral curves of Hamiltonian systems, pseudodifferential equations and canonical transformations, subelliptic operators and Poisson brackets. The second survey written by V.Ya. Ivrii treats linear hyperbolic equations and systems. The author states necessary and sufficient conditions for C?- and L2 -well-posedness and he studies the analogous problem in the context of Gevrey classes. He also gives the latest results in the theory of mixed problems for hyperbolic operators and a list of unsolved problems. Both parts cover recent research in an important field, which before was scattered in numerous journals. The book will hence be of immense value to graduate students and researchers in partial differential equations and theoretical physics.

• Ausbreitung von Singularitäten
• C and L2 well posedness of the Cauchy problem
• Fourier integral operators
• Fourier-Integraloperatoren
• Gevrey classes
• Gevreysche Klassen
• Hamiltonian systems
• Hamiltonsche Systeme
• Hyperbolische Operatoren
• Hypoelliptizitä
• Microlocal analysis
• Theoretical physics
• calculus
• hyperbolic equation
• partial differential equation

• Department of Mathematics, Moscow State University, Leninskie Gory, Moscow, Russia

  Yu. V. Egorov, M. A. Shubin

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