Stegall's smooth variational principle

Marian Fabian
Czech Academy of Science/Mathematics
fabian@karlin.mff.cuni.cz

ABSTRACT. We make a propaganda for a simple and powerful Stegall's variational principle: Let X be a reflexive, or more generally, dentable Banach space and f: X -->(-infinity,+infinity ] be a bounded below, lower semicontinuous, and coercive function. Then, given epsilon>0, there is a linear continuous functional xi on X such that |xi|<epsilon and f-xi attains a minimum at some point. We show how to use this principle in some smoothness questions occurring in Banach spaces, in particular in lp spaces.

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