Direct methods in the calculus of variations /
A comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well-known and were widely-used...
| Основен автор: | Giusti, Enrico. |
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| Формат: | Електронна книга |
| Език: | English |
| Публикувано: |
River Edge, NJ :
World Scientific,
℗♭2003.
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| Предмети: | |
| Онлайн достъп: |
http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235657 |
| Подобни документи: |
Print version::
Direct methods in the calculus of variations. |
| Резюме: |
A comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well-known and were widely-used in the 20th century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this work, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The volume is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory. |
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| Физически характеристики: |
1 online resource (vii, 403 pages) |
| Библиография: |
Includes bibliographical references (pages 377-398) and index. |
| ISBN: |
9789812795557 9812795553 1281935905 9781281935908 |