Résumé
This book is devoted to an invariant multidimensional
process of recovering a function from its derivative. It
considers additive functions defined on the family of all
bounded BV sets that are continuous with respect to a
suitable topology. A typical example is the flux of a
continuous vector field. A very general Gauss-Green theorem
follows from the sufficient conditions for the derivability
of the flux. Since the setting is invariant with respect to
local lipeomorphisms, a standard argument extends the
Gauss-Green theorem to the Stokes theorem on Lipschitz
manifolds. In addition, the author proves the Stokes
theorem for a class of top-dimensional normal currents - a
first step towards solving a difficult open problem of
derivation and integration in middle dimensions. The book
contains complete and detailed proofs of all new results,
and of many known results for which the references are not
easily available. It will provide valuable information to
research mathematicians and advanced graduate students
interested in geometric integration and related areas.
Contents
- Preface
- Acknowledgements
- 1 Preliminaries 1
- 2 Charges 47
- 3 Variations of charges 90
- 4 Charges and BV functions 135
- 5 Integration 186
- 6 Extending the integral 229
- Bibliography 255
- List of symbols 259
- Index 263
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Cambridge University Press |
| Auteur(s) | Washek F. Pfeffer |
| Parution | 16/10/2001 |
| Nb. de pages | 266 |
| Format | 15,5 x 23,5 |
| Couverture | Relié |
| Poids | 551g |
| Intérieur | Noir et Blanc |
| EAN13 | 9780521792684 |
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