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Second order estimates on transition layers for the Allen-Cahn equation with homogeneous Neumann boundary conditions: Part I - Boundary-orthogonal transition layers
We study stable solutions of the Allen-Cahn equation with homogeneous Neumann boundary condition on Riemannian manifolds with boundary in the regime where the transition layers meet the boundary orthogonally. Under an a priori bound for the enhanced second fundamental form in the transition region,
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