Singular perturbation of a class of non-convex functionals

✍ Scribed by Xinwei Yu; Zhiping Li; Lung-an Ying

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 217 KB
• Volume: 52
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(02)00156-6

✦ Synopsis

Models involving singular perturbation to a non-convex potential energy play a very important role in describing phase transitions, e.g. the celebrated Cahn-Hillard model where a two-well potential energy functional (i.e., the potential has two zeros) is perturbed by the L 2 -norm of the gradient.

Many variants of this model have been studied. In this paper, we perturb a general multi-well energy functional by the L 2 -norm of a higher gradient Hessian of arbitrary order and study its (L 1 )-limit. As expected, the limit functional assigns di erent surface energy densities to interfaces between di erent phases and computes the total energy.