Weak Continuity and Weak Lower Semicontinuity of Non-Linear Functionals by Bernard Dacorogna
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Weak Continuity and Weak Lower Semicontinuity of Non-Linear Functionals written by
Bernard Dacorogna
The notes are divided in three chapters. The first one studies various necessary and sufficient conditions so that the function f is weakly continuous or weakly lower semicontinuous; these conditions will depend strongly on the type of bounds on the derivatives of the sequence {u e} one assumes. In the context of the calculus of variations the problem of specifying conditions of this type has received considerable attention and some of the results presented here go as far back as Hadamard ([Hal], [Ha2]). Recently Murat and Tartar ([Mul]-[}~3], [Tal], [Ta2]) have set the problem in a more general context; they assume some boundedness on some combinations of the derivatives of u e, which are mere general than those of the calculus of variations.
Book Detail :-
Title: Weak Continuity and Weak Lower Semicontinuity of Non-Linear Functionals
Edition:
Author(s): Bernard Dacorogna
Publisher: Springer-Verlag Berlin Heidelberg
Series: Lecture Notes in Mathematics 922
Year: 1982
Pages: 125
Type: PDF
Language: English
ISBN: 978-3-540-11488-8,978-3-540-39171-5
Country: Switzerland
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About Author :-
The author Bernard Dacorogna is a PHD and Professor Emeritus of Statistics at the University of Florida. He is the author of Advanced Calculus with Applications in Statistics, Second Edition and co-author of Statistical Tests for Mixed Linear Models, all published by Wiley. Dr. Khuri is a member of numerous academic associations, among them the American Statistical Association and the Institute of Mathematical Statistics.
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Book Contents :-
Vector Valued Partial Differential Equations and Applications written by
Bernard Dacorogna, Nicola Fusco, Stefan Müller, Vladimir Sverak, John Ball, Paolo Marcellini
cover the following topics.
Introduction
I. Compensated Compactness
II. Applications
III. Dual and Relaxed Problems
Appendix
References
Index
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