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008 121227s2004 gw | s |||| 0|eng d
020 _a9783540409151
_9978-3-540-40915-1
024 7 _a10.1007/b96984
_2doi
050 4 _aQA315-316
050 4 _aQA402.3
050 4 _aQA402.5-QA402.6
072 7 _aPBKQ
_2bicssc
072 7 _aMAT005000
_2bisacsh
072 7 _aPBKQ
_2thema
072 7 _aPBU
_2thema
082 0 4 _a515.64
_223
100 1 _aReichel, Wolfgang.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aUniqueness Theorems for Variational Problems by the Method of Transformation Groups
_h[electronic resource] /
_cby Wolfgang Reichel.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2004.
300 _aXIV, 158 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1841
505 0 _aIntroduction -- Uniqueness of Critical Points (I) -- Uniqueness of Citical Pints (II) -- Variational Problems on Riemannian Manifolds -- Scalar Problems in Euclidean Space -- Vector Problems in Euclidean Space -- Fréchet-Differentiability -- Lipschitz-Properties of ge and omegae.
520 _aA classical problem in the calculus of variations is the investigation of critical points of functionals {\cal L} on normed spaces V. The present work addresses the question: Under what conditions on the functional {\cal L} and the underlying space V does {\cal L} have at most one critical point? A sufficient condition for uniqueness is given: the presence of a "variational sub-symmetry", i.e., a one-parameter group G of transformations of V, which strictly reduces the values of {\cal L}. The "method of transformation groups" is applied to second-order elliptic boundary value problems on Riemannian manifolds. Further applications include problems of geometric analysis and elasticity.
650 0 _aMathematical optimization.
650 0 _aDifferential equations, partial.
650 1 4 _aCalculus of Variations and Optimal Control; Optimization.
_0http://scigraph.springernature.com/things/product-market-codes/M26016
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540218395
776 0 8 _iPrinted edition:
_z9783662175231
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1841
856 4 0 _uhttps://doi.org/10.1007/b96984
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11819
_d11819