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Uniqueness Theorems for Variational Problems by the Method of Transformation Groups (Lecture Notes in Mathematics, 1841) - Softcover
Synopsis
A 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.
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About the Author
Studies:
October 1987 -- January 1994 Diplom studies in mathematics at the University of Karlsruhe
October 1991 -- October 1992 Master of Science in nonlinear mathematics, University of Bath (U.K.)
Phd: January 1996 University of Karlsruhe
Habilitation: October 2001 University of Basel
Positions held:
March 1994 -- June 1998 Scientific collaborator, Math. Institute, Univ. of Karlsruhe
October 1998 -- September 2002 Assistant, Math. Institute, University of Basel
Sommersemester 2000: Lecturer at the Univ. of Zurich
Wintersemester 2002/2003: Substitute professor at the Univ. of Giessen
Since April 2003: Substitute professor at the Univ. of Basel
Stays at other institutions:
October 1996 -- September 1998: postdoc at the Univ. of Minnesota (USA) and Univ. of Cologne with DFG-grant
March,July, August 1999: visitor at the Univ. of Cardiff (U.K) with EPSRC-grant
Awards: April 1997: "Klaus-Tschira Price for comprehensible science" awarded for the doctoral thesis by the Univ. of Karlsruhe
"About this title" may belong to another edition of this title.
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Uniqueness theorems for variational problems by the method of transformation groups. Lecture Notes in Mathematics; 1841.
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Uniqueness Theorems for Variational Problems by the Method of Transformation Groups
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Kartoniert / Broschiert. Condition: New. Includes supplementary material: sn.pub/extrasStudies: October 1987 -- January 1994 Diplom studies in mathematics at the University of KarlsruheOctober 1991 -- October 1992 Master of Science in nonlinear mathematics, University of Bath. Seller Inventory # 4885232
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Uniqueness Theorems for Variational Problems by the Method of Transformation Groups
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Taschenbuch. Condition: Neu. Neuware - A classical problem in the calculus of variations is the investigation ofcritical 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. Seller Inventory # 9783540218395
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