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On the construction of minimizing sequences for convex functionals with upper and lower bounding functionals
Author(s) -
Smith P.,
Roach G. F.
Publication year - 1981
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670030114
Subject(s) - mathematics , bounding overwatch , regular polygon , operator (biology) , upper and lower bounds , laplace operator , sequence (biology) , class (philosophy) , convex function , pure mathematics , combinatorics , mathematical analysis , geometry , transcription factor , gene , biochemistry , chemistry , genetics , repressor , artificial intelligence , biology , computer science
A method is described for constructing upper and lower bounds for the stationary values of a general class of convex functionals. The method relies of the existence of approximating convex functionals whose Gâteaux derivatives are presumed to have simpler structure than the original. The method is iterative in that convergent sequences of bounds can be constructed. Some applications to the Laplacian operator are included.