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Plateau Angle Conditions for the Vector-Valued Allen--Cahn Equation
Nicholas D. Alikakos, Panagiotis Antonopoulos, Apostolos Damialis
Source abstract
Under proper hypotheses, we rigorously derive the Plateau angle conditions at triple junctions of diffused interfaces in three dimensions, starting from the vector-valued Allen--Cahn equation with a triple-well potential. Our derivation is based on an application of the divergence theorem using the divergence-free form of the equation via an associated stress tensor.
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