Density Estimates for Ginzburg–Landau Energies with Degenerate Double-Well Potentials
Abstract
Abstract. We consider a class of Allen–Cahn equations associated with Ginzburg–Landau energies involving degenerate double-well potentials that vanish of order [Formula: see text] at the minima [Formula: see text] and establish density estimates for the level sets of nontrivial minimizers [Formula: see text]. This extends a result of Dipierro–Farina–Valdinoci where the density estimates for such degenerate potentials were obtained for a bounded range of [Formula: see text]’s. The original estimates for the classical case [Formula: see text] were established by Caffarelli–Córdoba.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Solidification and crystal growth phenomena
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 3
- Pages
- 2965–2976
- Publication date
- 10 June 2026
- Language
- EN