An Introduction to Γ-Convergence

✍ Scribed by Gianni Dal Maso (auth.)

• Publisher: Birkhäuser Basel
• Year: 1993
• Tongue: English
• Leaves: 351
• Series: Progress in Nonlinear Differential Equations and Their Applications 8
• Edition: 1
• Category: Library

✦ Table of Contents

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
Γ-convergence and K-convergence....Pages 38-45
Comparison with Pointwise Convergence....Pages 46-52
Some Properties of Γ-limits....Pages 53-66
Convergence of Minima and of Minimizers....Pages 67-85
Sequential Characterization of Γ-limits....Pages 86-100
Γ-convergence in Metric Spaces....Pages 101-110
The Topology of Γ-convergence....Pages 111-125
Γ-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
$$ \bar{\Gamma } $$ -convergence of Increasing Functionals....Pages 181-188
The Topology of $$ \bar{\Gamma } $$ -convergence....Pages 189-201
The Fundamental Estimate....Pages 202-207
Local Functionals and the Fundamental Estimate....Pages 208-214
Integral Representation of Γ-limits....Pages 215-222
Boundary Conditions....Pages 223-228
G-convergence of Elliptic Operators....Pages 229-238
Translation Invariant Functionals....Pages 239-246
Homogenization....Pages 247-255
Some Examples in Homogenization....Pages 256-263
Back Matter....Pages 265-341

✦ Subjects

Difference and Functional Equations