×

Variational analysis in Sobolev and BV spaces. Applications to PDEs and optimization. 2nd revised ed. (English) Zbl 1311.49001

It is an extended second edition of this well–written and self–contained book. The book is an excellent source of information for anyone interested in variational analysis, optimization, and PDEs. It is divided into two parts. The first one – Basic Variational Principles and the second one – Advanced Variational Analysis. The first part in chapters 1-9 covers the following subjects: weak solution methods, abstract variational principles, complements on measure theory, Sobolev spaces, classical examples, the finite element method, spectral analysis, convex duality and optimization. The second part in chapters 10–17 presents the following subjects: BV and SBV spaces, relaxation in Sobolev, BV, and Young measures spaces, \(\Gamma\)-convergence and applications, integral functionals of the calculus of variations, applications in mechanics and computer vision, variational problems with a lack of coercivity, shape optimization problems and gradient flows.
The book is addressed to PhD students, researchers and practicioners who want to study the field of variational analysis in a systematic way. Summing up, everybody who is interested in variational methods, optimization, and PDEs should have this valuable book in his/her library.

MSC:

49-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control
49K20 Optimality conditions for problems involving partial differential equations
49J45 Methods involving semicontinuity and convergence; relaxation
49J52 Nonsmooth analysis
49Q10 Optimization of shapes other than minimal surfaces
49Q20 Variational problems in a geometric measure-theoretic setting
90C48 Programming in abstract spaces

Citations:

Zbl 1095.49001
PDFBibTeX XMLCite
Full Text: DOI