Variational Principles for Second-order Differential Equations

Released on by J. Grifone
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  • Variational Principles for Second-order Differential Equations Book Detail

  • Author : J. Grifone
  • Release Date : 2000
  • Publisher : World Scientific
  • Genre : Mathematics
  • Pages : 236
  • ISBN 13 : 9789810237349
  • File Size : 15,15 MB
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Variational Principles for Second-order Differential Equations by J. Grifone PDF Summary

Book Description: The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler-Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi-Civita for some Riemann metric.To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer-Quillen-Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc.

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