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20162026
most citedOn Ambrosetti-Malchiodi-Ni conjecture on two-dimensional smooth bounded domains: clustering concentration layers

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math.AP2020

Clustering of Boundary Interfaces for an inhomogeneous Allen-Cahn equation on a smooth bounded domain

Lipeng Duan, Suting Wei, Jun Yang

We consider the inhomogeneous Allen-Cahn equation $$ ε^2Δu\,+\,V(y)(1-u^2)\,u\,=\,0\quad \mbox{in}\ Ω, \qquad \frac {\partial u}{\partial ν}\,=\,0\quad \mbox{on}\ \partial Ω, $$ wh…