Convex analysis | Calculus of variations | Theorems in functional analysis

Tonelli's theorem (functional analysis)

In mathematics, Tonelli's theorem in functional analysis is a fundamental result on the weak lower semicontinuity of nonlinear functionals on Lp spaces. As such, it has major implications for functional analysis and the calculus of variations. Roughly, it shows that weak lower semicontinuity for integral functionals is equivalent to convexity of the integral kernel. The result is attributed to the Italian mathematician Leonida Tonelli. (Wikipedia).

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Related pages

Functional (mathematics) | Convex function | Weak topology | If and only if | Dimension | Functional analysis | Extended real number line | Leonida Tonelli | Lp space | Mathematics | Calculus of variations | Domain (mathematical analysis) | Euclidean space | Continuous function | Semi-continuity