Tonelli's theorem (functional analysis)

This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources. Find sources: "Tonelli's theorem" functional analysis – news · newspapers · books · scholar · JSTOR (January 2013)

In mathematics, Tonelli's theorem in functional analysis is a fundamental result on the weak lower semicontinuity of nonlinear functionals on L^p 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.