000			03998nam a22004335i 4500
001			978-0-387-70914-7
003			DE-He213
005			20250710084011.0
007			cr nn 008mamaa
008			101109s2010 xxu| s |||| 0|eng d
020			_a9780387709147 _a99780387709147
024	7		_a10.1007/978-0-387-70914-7 _2doi
082	0	4	_a515.7 _223
100	1		_aBrezis, Haim. _eauthor.
245	1	0	_aFunctional Analysis, Sobolev Spaces and Partial Differential Equations _h[recurso electrónico] / _cby Haim Brezis.
264		1	_aNew York, NY : _bSpringer New York, _c2010.
300			_aXIV, 600p. 9 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _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 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c58183 _d58183