Mean Value Inequalities in Hilbert Space
Open Access
- 1 July 1994
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 344 (1) , 307-324
- https://doi.org/10.2307/2154718
Abstract
We establish a new mean value theorem applicable to lower semi-continuous 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
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