Description
Functional Analysis, Sobolev Spaces, and Calculus of Variations, 1st ed. 2024
La Matematica per il 3+2 Series
Language: EnglishSubject for Functional Analysis, Sobolev Spaces, and Calculus of...:
Keywords
Banach space; Hilbert space; Lebesgue space; Sobolev space; weak topology; convex analysis; weak lower semicontinuity; direct method; Lax-Milgram lemma; Hahn-Banach theorem; Banach-Steinhauss principle; open-mapping theorem; closed-graph theorem; adjoint operator; compact operator; Fourier transform; Poincaré's inequality; Sobolev inequalities; optimality conditions
387 p. · 15.5x23.5 cm · Paperback
Description
/li>Contents
/li>Biography
/li>Comment
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1 Motivation and perspective.- Part I: Basic Functional Analysis and Calculus of Variations.- 2 A first exposure to Functional Analysis.- 3 Introduction to convex analysis. The Hahn-Banach and Lax-Milgram theorems.- 4 The Calculus of Variations for one-dimensional problems.- Part II: Basic Operator Theory.- 5 Continuous operators.- 6 Compact operators.- Part III: Multidimensional Sobolev Spaces and Scalar Variational Problems.- 7 Multidimensional Sobolev spaces.- 8 Variational problems.- 9 Finer results in Sobolev spaces and the Calculus of Variations.- Appendix A: Hints and solutions to exercises.- Appendix B: So much to learn.
Covers, in a single source, the full road to treat standard variational problems in solid analytical foundation
The style facilitates progressive understanding, while the set of solved exercises helps in maturing concepts
Reference text for an introduction to Functional Analysis, Sobolev spaces or Calculus of Variations