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024 7 $a10.1007/b96984
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100   $a20121227d2004      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aUniqueness Theorems for Variational Problems by the Method of Transformation Groups /$fby Wolfgang Reichel
205   $a1st ed. 2004.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2004.
215   $a1 online resource (XIV, 158 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1841
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-21839-4 
320   $aIncludes bibliographical references (pages [144]-149) and index.
327   $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.
330   $aA classical problem in the calculus of variations is the investigation of critical points of functionals {\cal L} on normed spaces V. The present work addresses the question: Under what conditions on the functional {\cal L} and the underlying space V does {\cal L} have at most one critical point? A sufficient condition for uniqueness is given: the presence of a "variational sub-symmetry", i.e., a one-parameter group G of transformations of V, which strictly reduces the values of {\cal L}. The "method of transformation groups" is applied to second-order elliptic boundary value problems on Riemannian manifolds. Further applications include problems of geometric analysis and elasticity.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1841
606   $aCalculus of variations
606   $aDifferential equations, Partial
606   $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
615  0$aCalculus of variations.
615  0$aDifferential equations, Partial.
615 14$aCalculus of Variations and Optimal Control; Optimization.
615 24$aPartial Differential Equations.
676   $a512
700   $aReichel$b Wolfgang$4aut$4http://id.loc.gov/vocabulary/relators/aut$0214785
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910144618903321
996   $aUniqueness theorems for variational problems by the method of transformation groups$9262667
997   $aUNINA