We consider the singularly perturbed problem Fε(u, Ω) : = ∫ Ωε| ∇ 2u| 2+ ε- 1| 1 - | ∇ u| 2| 2 on bounded domains Ω ⊂ R2. Under appropriate boundary conditions, we prove that if Ω is an ellipse, then the minimizers of Fε(· , Ω) converge to the viscosity solution of the eikonal equation | ∇ u| = 1 as ε→ 0.
Characterization of Minimizers of Aviles–Giga Functionals in Special Domains
Marconi E.
2021
Abstract
We consider the singularly perturbed problem Fε(u, Ω) : = ∫ Ωε| ∇ 2u| 2+ ε- 1| 1 - | ∇ u| 2| 2 on bounded domains Ω ⊂ R2. Under appropriate boundary conditions, we prove that if Ω is an ellipse, then the minimizers of Fε(· , Ω) converge to the viscosity solution of the eikonal equation | ∇ u| = 1 as ε→ 0.File in questo prodotto:
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