Plateau angle conditions for the vector-valued Allen-Cahn equation
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🧮 math.AP
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equationallen-cahnangleconditionsplateauvector-valuedapplicationassociated
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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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