Stable phase interfaces in the van der Waals–Cahn–Hilliard theory
-
Yoshihiro Tonegawa
and
Neshan Wickramasekera
Abstract
We prove that any limit-interface corresponding to a locally uniformly bounded, locally energy-bounded sequence of stable critical points of the van der Waals–Cahn–Hilliard energy functionals with perturbation parameter → 0+ is supported by an embedded stable minimal hypersurface which in low dimensions has no singularities and in general dimensions has possibly a closed singular set of co-dimension ≧ 7.
This result was previously known in case the critical points are local minimizers of energy, in which case the limit-interface is locally area minimizing and its (normalized) multiplicity is 1 a.e.
Our theorem uses earlier work of the first author establishing stability of the limit-interface as an integral varifold, and relies on a recent general theorem of the second author for its regularity conclusions in the presence of higher multiplicity.
©[2012] by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Overconvergent Witt vectors
- Special subvarieties of Drinfeld modular varieties
- Explicit uniform estimation of rational points I. Estimation of heights
- Explicit uniform estimation of rational points II. Hypersurface coverings
- Pieri rules for the K-theory of cominuscule Grassmannians
- The Hörmander multiplier theorem for multilinear operators
- Quantum cluster variables via Serre polynomials
- Stable phase interfaces in the van der Waals–Cahn–Hilliard theory
- On Brauer–Kuroda type relations of S-class numbers in dihedral extensions
Articles in the same Issue
- Overconvergent Witt vectors
- Special subvarieties of Drinfeld modular varieties
- Explicit uniform estimation of rational points I. Estimation of heights
- Explicit uniform estimation of rational points II. Hypersurface coverings
- Pieri rules for the K-theory of cominuscule Grassmannians
- The Hörmander multiplier theorem for multilinear operators
- Quantum cluster variables via Serre polynomials
- Stable phase interfaces in the van der Waals–Cahn–Hilliard theory
- On Brauer–Kuroda type relations of S-class numbers in dihedral extensions
