An Introduction to G-Convergence

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Springer Science & Business Media, 1993 - Mathematics - 340 pages
The last twentyfive years have seen an increasing interest for variational convergences and for their applications to different fields, like homogenization theory, phase transitions, singular perturbations, boundary value problems in wildly perturbed domains, approximation of variatonal problems, and non­ smooth analysis. Among variational convergences, De Giorgi's r-convergence plays a cen­ tral role for its compactness properties and for the large number of results concerning r -limits of integral functionals. Moreover, almost all other varia­ tional convergences can be easily expressed in the language of r -convergence. This text originates from the notes of the courses on r -convergence held by the author in Trieste at the International School for Advanced Studies (S. I. S. S. A. ) during the academic years 1983-84,1986-87, 1990-91, and in Rome at the Istituto Nazionale di Alta Matematica (I. N. D. A. M. ) during the spring of 1987. This text is far from being a treatise on r -convergence and its appli­ cations.

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Contents

II
4
IV
15
VI
24
VII
34
IX
42
XI
49
XIII
63
XV
82
XXXI
177
XXXIII
185
XXXV
198
XXXVI
204
XXXVIII
211
XL
219
XLII
225
XLIV
235

XVII
97
XIX
107
XXI
122
XXIII
129
XXV
144
XXVII
161
XXIX
170
XLVI
243
XLVII
252
XLIX
261
L
285
LI
335
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