Hedy Attouch

Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization, Second Edition

Preface to the second edition Preface to the first edition 1. Introduction Part I. Basic Variational Principles: 2. Weak solution methods in variational analysis 3. Abstract variational principles 4. Complements on measure theory 5. Sobolev spaces 6. Variational problems: some classical examples 7. The finite element method 8. Spectral analysis of the Laplacian 9. Convex duality and optimization Part II. Advanced Variational Analysis: 10. Spaces BV and SBV 11. Relaxation in Sobolev, BV, and Young measure spaces 12. GAMMA-Convergence and applications 13. Integral functionals of the calculus of variations 14. Applications in mechanics and computer vision 15. Variational problems with a lack of coercivity 16. An introduction to shape optimization problems 17. Gradient flows Bibliography Index.