Functional Analysis, Sobolev Spaces, and Calculus of Variations
Springer International Publishing (Verlag)
978-3-031-49245-7 (ISBN)
lt;b>Pablo Pedregal received his Ph.D. degree in Mathematics from the University of Minnesota at the end of 1989, under the guidance of D. Kinderlehrer. Soon after that, he became Associate Professor at U. Complutense. During the academic year 1994-95 he moved to U. de Castilla-La Mancha where he led the Math Department for several years. In 1997 he became full professor. His field of interest focuses on variational techniques applied to optimization in a broad sense, including, but not limited to, calculus of variations-especially vector, non-convex problems-, optimal design in continuous media, optimal control, etc, and more recently he has explored variational ideas in areas like inverse problems, and dynamical systems, as well as optimal control problems governed by hyper-elasticity. He has regularly traveled to research centers in the USA and Europe. He has written more than one hundred research articles, seven specialized books (at least three of them with Springer), and some other of a more didactic style for undergraduates.
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.
Erscheinungsdatum | 01.02.2024 |
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Reihe/Serie | La Matematica per il 3+2 | UNITEXT |
Zusatzinfo | XIV, 387 p. |
Verlagsort | Cham |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 756 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
Schlagworte | adjoint operator • Banach space • Banach-Steinhauss principle • closed-graph theorem • Compact operator • Convex Analysis • Direct Method • Fourier transform • Hahn-Banach theorem • hilbert space • Lax-Milgram lemma • Lebesgue Space • open-mapping theorem • Optimality conditions • Poincaré's inequality • Sobolev inequalities • Sobolev Space • weak lower semicontinuity • Weak topology |
ISBN-10 | 3-031-49245-5 / 3031492455 |
ISBN-13 | 978-3-031-49245-7 / 9783031492457 |
Zustand | Neuware |
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