MINIMIZERS AND THE EULER-LAGRANGE EQUATIONS.

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Abstract

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.

Original languageEnglish
Title of host publicationLecture Notes in Physics
Pages1-4
Number of pages4
Edition195
Publication statusPublished - 1984

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  • Cite this

    Ball, J. M. (1984). MINIMIZERS AND THE EULER-LAGRANGE EQUATIONS. In Lecture Notes in Physics (195 ed., pp. 1-4)