Boundary Effects in the Gradient Theory of Phase Transitions

@article{Bertini2011BoundaryEI,
  title={Boundary Effects in the Gradient Theory of Phase Transitions},
  author={Lorenzo Bertini and Paolo Butt{\`a} and Adriana Garroni},
  journal={SIAM J. Math. Anal.},
  year={2011},
  volume={44},
  pages={926-945}
}
We consider the van der Waals' free energy functional, with a scaling small parameter epsilon, in the plane domain given by the first quadrant, and inhomogeneous Dirichlet boundary conditions. The boundary data are chosen in such a way that the interface between the pure phases tends to be horizontal and is pinned at some point on the y-axis which approaches zero as epsilon converges to zero. We show that there exists a critical scaling for the pinning point, such that, as the small parameter… 

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