Ebook: An Introduction to Γ-Convergence

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Content:
Front Matter....Pages i-xiv
Introduction....Pages 1-7
The Direct Method in the Calculus of Variations....Pages 8-18
Minimum Problems for Integral Functionals....Pages 19-27
Relaxation....Pages 28-37
?-convergence and K-convergence....Pages 38-45
Comparison with Pointwise Convergence....Pages 46-52
Some Properties of ?-limits....Pages 53-66
Convergence of Minima and of Minimizers....Pages 67-85
Sequential Characterization of ?-limits....Pages 86-100
?-convergence in Metric Spaces....Pages 101-110
The Topology of ?-convergence....Pages 111-125
?-Convergence in Topological Vector Spaces....Pages 126-132
Quadratic Forms and Linear Operators....Pages 133-147
Convergence of Resolvents and G-convergence....Pages 148-164
Increasing Set Functions....Pages 165-173
Lower Semicontinuous Increasing Functionals....Pages 174-180
The Fundamental Estimate....Pages 181-188
Local Functionals and the Fundamental Estimate....Pages 189-201
Integral Representation of ?-limits....Pages 202-207
Boundary Conditions....Pages 208-214
G-convergence of Elliptic Operators....Pages 215-222
Translation Invariant Functionals....Pages 223-228
Homogenization....Pages 229-238
Some Examples in Homogenization....Pages 239-246
Back Matter....Pages 247-255
....Pages 256-263