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Linear functionals on nonlinear spaces and applications to problems from viscoplasticity theory

✍ Scribed by Waldemar Pompe

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 149 KB
Volume: 31
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.943

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✦ Synopsis

Abstract

A classical result in the theory of monotone operators states that if C is a reflexive Banach space, and an operator A: C→C^*^ is monotone, semicontinuous and coercive, then A is surjective. In this paper, we define the ‘dual space’ C^*^ of a convex, usually not linear, subset C of some Banach space X (in general, we will have C^*^⊃X^*^) and prove an analogous result. Then, we give an application to problems from viscoplasticity theory, where the natural space to look for solutions is not linear. Copyright © 2007 John Wiley & Sons, Ltd.

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