Calculus of Variations

Front Cover
Cambridge University Press, 1998 - Mathematics - 323 pages
This textbook on the calculus of variations leads the reader from the basics to modern aspects of the theory. One-dimensional problems and the classical issues such as Euler-Lagrange equations are treated, as are Noether's theorem, Hamilton-Jacobi theory, and in particular geodesic lines, thereby developing some important geometric and topological aspects. The basic ideas of optimal control theory are also given. The second part of the book deals with multiple integrals. After a review of Lebesgue integration, Banach and Hilbert space theory and Sobolev spaces (with complete and detailed proofs), there is a treatment of the direct methods and the fundamental lower semicontinuity theorems. Subsequent chapters introduce the basic concepts of the modern calculus of variations, namely relaxation, Gamma convergence, bifurcation theory and minimax methods based on the Palais-Smale condition. The prerequisites are knowledge of the basic results from calculus of one and several variables. After having studied this book, the reader will be well equipped to read research papers in the calculus of variations.
 

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Contents

II
xv
IV
6
V
14
VI
20
VII
22
VIII
28
XI
39
XII
47
XLI
155
XLIV
162
XLVI
167
XLVII
171
XLIX
179
LII
180
LIII
183
LV
186

XIII
58
XV
63
XVI
75
XIX
77
XX
83
XXI
85
XXII
88
XXIII
91
XXIV
100
XXVI
102
XXVII
105
XXVIII
111
XXX
113
XXXIII
118
XXXIV
121
XXXVIII
128
XXXIX
140
XL
146
LVII
191
LVIII
201
LXI
209
LXIII
221
LXV
227
LXVI
231
LXVII
237
LXIX
244
LXX
253
LXXI
258
LXXIII
262
LXXVI
266
LXXVII
278
LXXIX
287
LXXXII
297
LXXXIII
302
LXXXIV
315
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