000			04351nam a22005295i 4500
001			978-0-8176-8313-9
003			DE-He213
005			20140220083228.0
007			cr nn 008mamaa
008			111111s2012 xxu| s |||| 0|eng d
020			_a9780817683139 _9978-0-8176-8313-9
024	7		_a10.1007/978-0-8176-8313-9 _2doi
050		4	_aQA370-380
072		7	_aPBKJ _2bicssc
072		7	_aMAT007000 _2bisacsh
082	0	4	_a515.353 _223
100	1		_aCsató, Gyula. _eauthor.
245	1	4	_aThe Pullback Equation for Differential Forms _h[electronic resource] / _cby Gyula Csató, Bernard Dacorogna, Olivier Kneuss.
264		1	_aBoston : _bBirkhäuser Boston, _c2012.
300			_aXI, 436p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aProgress in Nonlinear Differential Equations and Their Applications ; _v83
505	0		_aIntroduction -- Part I Exterior and Differential Forms -- Exterior Forms and the Notion of Divisibility -- Differential Forms -- Dimension Reduction -- Part II Hodge-Morrey Decomposition and Poincaré Lemma -- An Identity Involving Exterior Derivatives and Gaffney Inequality -- The Hodge-Morrey Decomposition -- First-Order Elliptic Systems of Cauchy-Riemann Type -- Poincaré Lemma -- The Equation div u = f -- Part III The Case k = n -- The Case f × g > 0 -- The Case Without  Sign Hypothesis on f -- Part IV The Case 0 ≤ k ≤ n–1 -- General Considerations on the Flow Method -- The Cases k = 0 and k = 1 -- The Case k = 2 -- The Case 3 ≤ k ≤ n–1 -- Part V Hölder Spaces -- Hölder Continuous Functions -- Part VI Appendix -- Necessary Conditions -- An Abstract Fixed Point Theorem -- Degree Theory -- References -- Further Reading -- Notations -- Index. .
520			_aAn important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables. The problem is therefore to find a map φ so that it satisfies the pullback equation: φ*(g) = f.  In more physical terms, the question under consideration can be seen as a problem of mass transportation. The problem has received considerable attention in the cases k = 2 and k = n, but much less when 3 ≤ k ≤ n–1. The present monograph provides the first comprehensive study of the equation. The work begins by recounting various properties of exterior forms and differential forms that prove useful throughout the book. From there it goes on to present the classical Hodge–Morrey decomposition and to give several versions of the Poincaré lemma. The core of the book discusses the case k = n, and then the case 1≤ k ≤ n–1 with special attention on the case k = 2, which is fundamental in symplectic geometry. Special emphasis is given to optimal regularity, global results and boundary data. The last part of the work discusses Hölder spaces in detail; all the results presented here are essentially classical, but cannot be found in a single book. This section may serve as a reference on Hölder spaces and therefore will be useful to mathematicians well beyond those who are only interested in the pullback equation. The Pullback Equation for Differential Forms is a self-contained and concise monograph intended for both geometers and analysts. The book may serve as a valuable reference for researchers or a supplemental text for graduate courses or seminars.
650		0	_aMathematics.
650		0	_aMatrix theory.
650		0	_aDifferential Equations.
650		0	_aDifferential equations, partial.
650		0	_aGlobal differential geometry.
650	1	4	_aMathematics.
650	2	4	_aPartial Differential Equations.
650	2	4	_aLinear and Multilinear Algebras, Matrix Theory.
650	2	4	_aDifferential Geometry.
650	2	4	_aOrdinary Differential Equations.
700	1		_aDacorogna, Bernard. _eauthor.
700	1		_aKneuss, Olivier. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817683122
830		0	_aProgress in Nonlinear Differential Equations and Their Applications ; _v83
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-8313-9
912			_aZDB-2-SMA
999			_c100241 _d100241