000 04025nam a22004575i 4500
001 978-0-387-70914-7
003 DE-He213
005 20140220083710.0
007 cr nn 008mamaa
008 101109s2011 xxu| s |||| 0|eng d
020 _a9780387709147
_9978-0-387-70914-7
024 7 _a10.1007/978-0-387-70914-7
_2doi
050 4 _aQA319-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
082 0 4 _a515.7
_223
100 1 _aBrezis, Haim.
_eauthor.
245 1 0 _aFunctional Analysis, Sobolev Spaces and Partial Differential Equations
_h[electronic resource] /
_cby Haim Brezis.
264 1 _aNew York, NY :
_bSpringer New York,
_c2011.
300 _aXIV, 600p. 9 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext
505 0 _aPreface -- 1. The Hahn–Banach Theorems. Introduction to the Theory of Conjugate Convex Functions -- 2. The Uniform Boundedness Principle and the Closed Graph Theorem. Unbounded Operators. Adjoint. Characterization of Surjective Operators -- 3. Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity -- 4. L^p Spaces -- 5. Hilbert Spaces -- 6. Compact Operators. Spectral Decomposition of Self-Adjoint Compact Operators -- 7. The Hille–Yosida Theorem -- 8. Sobolev Spaces and the Variational Formulation of Boundary Value Problems in One Dimension -- 9. Sobolev Spaces and the Variational Formulation of Elliptic Boundary Value Problems in N Dimensions -- 10. Evolution Problems: The Heat Equation and the Wave Equation -- 11. Some Complements -- Problems -- Solutions of Some Exercises and Problems -- Bibliography -- Index.
520 _aUniquely, this book presents a coherent, concise and unified way of combining elements from two distinct “worlds,” functional analysis (FA) and partial differential equations (PDEs), and is intended for students who have a good background in real analysis. This text presents a smooth transition from FA to PDEs by analyzing in great detail the simple case of one-dimensional PDEs (i.e., ODEs), a more manageable approach for the beginner. Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Moreover, the wealth of exercises and additional material presented, leads the reader to the frontier of research. This book has its roots in a celebrated course taught by the author for many years and is a completely revised, updated, and expanded English edition of the important “Analyse Fonctionnelle” (1983). Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English version is a welcome addition to this list. The first part of the text deals with abstract results in FA and operator theory. The second part is concerned with the study of spaces of functions (of one or more real variables) having specific differentiability properties, e.g., the celebrated Sobolev spaces, which lie at the heart of the modern theory of PDEs. The Sobolev spaces occur in a wide range of questions, both in pure and applied mathematics, appearing in linear and nonlinear PDEs which arise, for example, in differential geometry, harmonic analysis, engineering, mechanics, physics etc. and belong in the toolbox of any graduate student studying analysis.
650 0 _aMathematics.
650 0 _aFunctional analysis.
650 0 _aDifferential equations, partial.
650 1 4 _aMathematics.
650 2 4 _aFunctional Analysis.
650 2 4 _aPartial Differential Equations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387709130
830 0 _aUniversitext
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-387-70914-7
912 _aZDB-2-SMA
999 _c105027
_d105027