Mean value inequalities in Hilbert space. (English) Zbl 0803.49018
Summary: We establish a new mean value theorem applicable to lower semicontinuous functions on Hilbert space. A novel feature of the result is its “multidirectionality”: it compares the value of a function at a point to its values on a set. We then discuss some refinements and consequences of the theorem, including applications to calculus, flow invariance, and generalized solutions to partial differential equations.
Keywords:
multidirectionality; lower semicontinuous functions; mean value theorem; flow invariance; inequalityReferences:
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