MINIMIZERS AND THE EULER-LAGRANGE EQUATIONS.

The paper discusses minimizing of certain equations. The problem of minimizing an integral subject to given boundary conditions, with a bounded open set and competing functions is discussed. Frequently it is possible to use the direct method of the calculus of variations to establish the existence of a minimizer u in an appropriate Sobolev space. Then formally it is expected that u satisfies the weak form of the Euler-Lagrange equiations, but a search of the literature reveals that in general the theorems quaranteeing this make stronger growth assumptions on f than are necessary to prove existence.