Namespaces
Variants
Actions

Potential operator

From Encyclopedia of Mathematics
Revision as of 17:22, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

A mapping of a Banach space into the dual space that is the gradient of some functional , i.e. is such that

For instance, any bounded self-adjoint operator defined on a Hilbert space is potential:

References

[1] M.M. Vainberg, "Variational method and method of monotone operators in the theory of nonlinear equations" , Wiley (1973) (Translated from Russian)
[2] H. Gajewski, K. Gröger, K. Zacharias, "Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen" , Akademie Verlag (1974)
How to Cite This Entry:
Potential operator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Potential_operator&oldid=48265
This article was adapted from an original article by V.I. Sobolev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article