Let $J$ be a sequentially weakly lower semicontinuous functional on $C$ with values on the real line. Moreover let $C$ be a bounded, closed and convex subset of a Hilbert space $H$.
Is it true that the functional attains his minimum?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this community
Some hints for the proof: