Loading...
Please wait, while we are loading the content...
Similar Documents
A sufficiency proof for isoperimetric problems in the calculus of variations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Hestenes, Magnus R. |
| Copyright Year | 1938 |
| Abstract | The purpose of the present paper is to show that the sufficiency theorems for a strong relative minimum for isoperimetric problems can be obtained from those for simple integral problems with only a little additional argument. The method here used is a simple extension of one used by Birkhoff and Hestenes* for a special isoperimetric problem. Heretofore sufficiency theorems of this type have been obtained from those for a restricted relative minimum by the application of the theorem of Lindeberg. Sufficiency theorems for a restricted relative minimum can be obtained either from the theories of the problems of Lagrange and Bolza or by an argument analogous to that used for simple integrals. The problem to be considered is that of minimizing an integral |
| Starting Page | 662 |
| Ending Page | 667 |
| Page Count | 6 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9904-1938-06838-3 |
| Alternate Webpage(s) | http://www.ams.org/journals/bull/1938-44-10/S0002-9904-1938-06838-3/S0002-9904-1938-06838-3.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9904-1938-06838-3 |
| Volume Number | 44 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
