## Introduction to Global Variational GeometryThis book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics - Analysis on manifolds - Differential forms on jet spaces - Global variational functionals - Euler-Lagrange mapping - Helmholtz form and the inverse problem - Symmetries and the Noether’s theory of conservation laws - Regularity and the Hamilton theory - Variational sequences - Differential invariants and natural variational principles - First book on the geometric foundations of Lagrange structures - New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity - Basic structures and tools: global analysis, smooth manifolds, fibred spaces |

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### Contents

15 | |

Chapter 2 LebesgueBesov Spaces without Weights in Rn and R+n | 151 |

Chapter 3 LebesgueBesov Spaces with Weigths in Domains | 245 |

Chapter 4 LebesgueBesov Spaces without Weigths in Domains | 309 |

Chapter 5 Regular Elliptic Differential Operators | 361 |

Chapter 6 Strongly Degenerate Elliptic Differential Operators | 405 |

Chapter 7 Legendre and Tricomi Differential Operators | 429 |

Chapter 8 Nuclear Function Spaces | 476 |

Bibliography | 483 |

Table of Symbols | 519 |

522 | |

527 | |

### Common terms and phrases

Banach spaces belongs Besov Besov spaces boundary value bounded C*-domain bounded domain compact compact operators consequence of Theorem considerations considered coretraction defined denotes dense eigenvalues elliptic differential operators embedding theorems equivalent norms estimate formula function spaces Further let GRISVARD Hayk CCCP Hence Hilbert spaces Hölder spaces holds infimum infinitesimal operator integer interpolation couple interpolation spaces interpolation theory isomorphic isomorphic mapping J. L. LIONs Lemma Let Q linear Lp(Q Lp(R Marem Matem Math method natural number obtains PEETRE positive number proof of Theorem properties prove pure point spectrum q soo real numbers regular elliptic Remark replace resp restriction right-hand side S(Rn Schauder basis self-adjoint self-adjoint operator semi-group sense of Definition ſº Sobolev spaces spaces B.A(R spaces with weights Subsection TRIEBEL valid weight function Whence it follows yields