Exterior Differential Systems and EulerLagrange Partial Differential Equations
216 pages

6 x 9

© 2003
Contents
Preface
Introduction
1. Lagrangians and PoincaréCartan Forms
1.1 Lagrangians and Contact Geometry
1.2 The EulerLagrange System
1.3 Noether's Theorem
1.4 Hypersurfaces in Euclidean Space
2. The Geometry of PoincaréCartan Forms
2.1 The Equivalence Problem for n = 2
2.2 NeoClassical PoincaréCartan Forms
2.3 Digression on Affine Geometry for Hypersurfaces
2.4 The Equivalence Problem for n > 3
2.5 The Prescribed Mean Curvature System
3. Conformally Invariant EulerLagrange Systems
3.1 Background Material on Conformal Geometry
3.2 Confromally Invariant PoincaréCartan Forms
3.3 The Conformal Branch of the Equivalence Problem
3.4 Conservation Laws for Du = Cu n+2/n2
3.5 Conservation Laws for Wave Equations
4. Additional Topics
4.1 The Second Variation
4.2 EulerLagrange PDE Systems
4.3 HigherOrder Conservation Laws
Introduction
1. Lagrangians and PoincaréCartan Forms
1.1 Lagrangians and Contact Geometry
1.2 The EulerLagrange System
1.3 Noether's Theorem
1.4 Hypersurfaces in Euclidean Space
2. The Geometry of PoincaréCartan Forms
2.1 The Equivalence Problem for n = 2
2.2 NeoClassical PoincaréCartan Forms
2.3 Digression on Affine Geometry for Hypersurfaces
2.4 The Equivalence Problem for n > 3
2.5 The Prescribed Mean Curvature System
3. Conformally Invariant EulerLagrange Systems
3.1 Background Material on Conformal Geometry
3.2 Confromally Invariant PoincaréCartan Forms
3.3 The Conformal Branch of the Equivalence Problem
3.4 Conservation Laws for Du = Cu n+2/n2
3.5 Conservation Laws for Wave Equations
4. Additional Topics
4.1 The Second Variation
4.2 EulerLagrange PDE Systems
4.3 HigherOrder Conservation Laws
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