| Review: |
This book provides a systematic and comprehensive guide to variational analysis, beginning with classical examples and working up to research level. The aim of the book is twofold: the first is to provide graduate-level students with the basic tools and methods of variational analysis and optimisation in infinite dimensional spaces, together with applications to classical PDE problems. The second objective is to present new trends in variational analysis and some of the most recent developments and applications. There are chapters on: weak solution methods in variational analysis; abstract variational principles; complements on measure theory; Sobolev spaces; variational problems; the finite element method; spectral analysis of the Laplacian; convex duality and optimisation; spaces BV and SBV; relaxation in Sobolev, BV, and Young measure spaces; integral functionals of the calculus of variations; applications in mechanics and computer vision; and variational problems with a lack of coercivity. |