We prove the following results: 1. A unique smooth solution exists for a short time for the heat equation associated with the Möbius energy of loops in a euclidean space, starting with any simple smooth loop. 2. A critical loop of the energy is smooth if it has cube-integrable curvature. Combining
On the Validity of the Euler–Lagrange Equation
✍ Scribed by Arrigo Cellina
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 137 KB
- Volume
- 171
- Category
- Article
- ISSN
- 0022-0396
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