Uniform Lipschitz regularity of flat segregated interfaces in a singularly perturbed problem

Abstract

For the singularly perturbed system \[Δu_{i,β}=βu_{i,β}\sum_{j\neq i}u_{j,β}^2, \quad 1\leq i\leq N,\] we prove that flat interfaces are uniformly Lipschitz. As a byproduct of the proof we also obtain the optimal lower bound near the flat interfaces, \[\sum_iu_{i,β}\geq cβ^{-1/4}.\]

11 pages

References in corpus (3)

• Uniform bounds for strongly competing systems: the optimal Lipschitz case
• On phase separation in systems of coupled elliptic equations: asymptotic analysis and geometric aspects
• A new proof of Savin's theorem on Allen-Cahn equations