Buch, Englisch, 270 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 575 g
An Introduction
Buch, Englisch, 270 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 575 g
ISBN: 978-0-19-850465-8
Verlag: OUP Oxford
One-dimensional variational problems have been somewhat neglected in the literature on calculus of variations, as authors usually treat minimal problems for multiple integrals which lead to partial differential equations and are considerably more difficult to handle. One-dimensional problems are connected with ordinary differential equations, and hence need many fewer technical prerequisites, but they exhibit the same kind of phenomena and surprises as variational problems for multiple integrals. This book provides an modern introduction to this subject, placing special emphasis on direct methods. It combines the efforts of a distinguished team of authors who are all renowned mathematicians and expositors. Since there are fewer technical details graduate students who want an overview of the modern approach to variational problems will be able to concentrate on the underlying theory and hence gain a good grounding in the subject. Except for results from the theory of measure and integration and from the theory of convex functions, the text develops all mathematical tools needed, including the basic results on one-dimensional Sobolev spaces, absolutely continuous functions, and functions of bounded variation.
Autoren/Hrsg.
Weitere Infos & Material
- Introduction
- 1: Classical problems and indirect methods
- 2: Absolutely continuous functions and Sobolev spaces
- 3: Semicontinuity and existence results
- 4: Regularity of minimizers
- 5: Some applications
- 6: Scholia
