Lectures on Functional Analysis and Applications - Igor Sinitsyn,V S Pugachev
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Saadetis 22-28 tööpäeva jooksul
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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 c ... Täielik kirjeldus
Kirjeldus
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.
Lisateave
| Autor | Igor Sinitsyn, V S Pugachev |
|---|---|
| Kirjastaja | World Scientific Publishing Company |
| Väljalaskeaasta | 1999 |
| Kaanetüüp | Kõvakaaneline |
| EAN | 9789810237226 |