01270nam0-22004091i-450-99000550139020331620020123120000.0000550139USA01000550139(ALEPH)000550139USA0100055013920020123d2001-------|0itac50------baitaIT||||I |||||Bilanci consuntivi delle amministrazioni comunalianno 1997Istituto centrale di statisticaRomaISTAT200137 p.tab.25 cmdischetti da 3,5".Informazioni92001USA46172001Informazioni9Enti localibilancio -ItaliaFIRoma352.17Contabilità e revisione dei conti21Istituto centrale di statistica374421istatITSOL20120104990005501390203316DIP.TO SCIENZE ECONOMICHE - (SA)DS 300 352.17 istssn464 DISES300 352.17 ist464 DISESBKDISES20121027USA01153220121027USA011613Bilanci consuntivi delle amministrazioni comunali1127681UNISAUSA1089703749nam 22006735 450 991014629220332120250801064914.03-540-69594-X10.1007/BFb0092831(CKB)1000000000437343(SSID)ssj0000326692(PQKBManifestationID)12069599(PQKBTitleCode)TC0000326692(PQKBWorkID)10296698(PQKB)10963532(DE-He213)978-3-540-69594-3(MiAaPQ)EBC5577146(MiAaPQ)EBC6691771(Au-PeEL)EBL5577146(OCoLC)1066180869(Au-PeEL)EBL6691771(PPN)155195549(EXLCZ)99100000000043734320121227d1997 u| 0engurnn#008mamaatxtccrSobolev Gradients and Differential Equations /by john neuberger1st ed. 1997.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1997.1 online resource (VIII, 152 p.)Lecture Notes in Mathematics,1617-9692 ;1670Bibliographic Level Mode of Issuance: Monograph3-540-63537-8 Includes bibliographical references (pages [145]-149) and index.Several gradients -- Comparison of two gradients -- Continuous steepest descent in Hilbert space: Linear case -- Continuous steepest descent in Hilbert space: Nonlinear case -- Orthogonal projections, Adjoints and Laplacians -- Introducing boundary conditions -- Newton's method in the context of Sobolev gradients -- Finite difference setting: the inner product case -- Sobolev gradients for weak solutions: Function space case -- Sobolev gradients in non-inner product spaces: Introduction -- The superconductivity equations of Ginzburg-Landau -- Minimal surfaces -- Flow problems and non-inner product Sobolev spaces -- Foliations as a guide to boundary conditions -- Some related iterative methods for differential equations -- A related analytic iteration method -- Steepest descent for conservation equations -- A sample computer code with notes.A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. Equal emphasis is placed on numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.Lecture Notes in Mathematics,1617-9692 ;1670Differential equationsNumerical analysisDifferential EquationsNumerical AnalysisDifferential equations.Numerical analysis.Differential Equations.Numerical Analysis.515/.35365N30msc35A15mscNeuberger J. W(John W.),1934-61864MiAaPQMiAaPQMiAaPQBOOK9910146292203321Sobolev gradients and differential equations374787UNINA