## 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 |

483 | |

Table of Symbols | 519 |

522 | |

527 | |

### Common terms and phrases

A0 A A1 assume Banach spaces Besov spaces bounded C°°-domain bounded domain CCCP coincides compact compact operators complex number consequence of Theorem considerations considered coretraction corresponding defined denotes dense domain of cone-type domain of definition eigenvalues elliptic differential operators embedding operators embedding theorems equivalent norms estimate exists a number extension formula function spaces Further let GRISVARD Hence Hilbert spaces holds infimum infinitesimal operator integer interpolation couple interpolation spaces interpolation theory isomorphic mapping J. L. LIONS Lebesgue spaces Lemma Let A0 Let Q linear MAGENES Math method natural number operator with pure PEETRE positive number proof of Theorem prove pure point spectrum real numbers regular elliptic Remark replace resp restriction retraction right-hand side Schauder basis second step Section self-adjoint operator semi-groups sense of Definition Sobolev spaces spaces A0 spaces with weights Subsection TRIEBEL valid weight function Whence it follows yields