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 |
|---|---|
| Title of host publication | Lecture Notes in Physics |
| Pages | 1-4 |
| Number of pages | 4 |
| Edition | 195 |
| Publication status | Published - 1984 |