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Bivariational and Singular Variational Derivatives
Author(s) -
Nashed M. Z.,
Hamilton E. P.
Publication year - 1990
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-41.3.526
Subject(s) - mathematics , pure mathematics , calculus (dental) , mathematical analysis , medicine , orthodontics
General representation theorems for the Gateaux differential of a functional on the space of continuous functions are established in terms of (locally defined) regular and singular variational derivatives. A new notion of singular bivariational derivative, which resolves difficulties inherent in the so‐called ‘exceptional’ points of Volterra, is introduced and studied.