Necessary conditions in the calculus of variations
Louise C. Young · Acta Mathematica · 1938
w I. Introduction.The object of this note is to introduce new variational methods, which belong to the order of ideas of MINKOWSKI'S theorem on the existence of a flat support for a convex figure.We here apply these methods to the inhomogeneous form of the >>simplest problem~ of the Calculus of Variations, and we establish, by means of them, a necessary condition, of a very general form, for an attained minimum.In the proof, an important part is also played by theorems of measurability which belong to the theory of Analytic and