### 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 language | English |
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Title of host publication | Lecture Notes in Physics |

Pages | 1-4 |

Number of pages | 4 |

Edition | 195 |

Publication status | Published - 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)