Quantization of the energy for the inhomogeneous Allen-Cahn mean curvature.

Math Ann

School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS UK.

Published: June 2024

We consider the varifold associated to the Allen-Cahn phase transition problem in (or -dimensional Riemannian manifolds with bounded curvature) with integral bounds on the Allen-Cahn mean curvature (first variation of the Allen-Cahn energy) in this paper. It is shown here that there is an equidistribution of energy between the Dirichlet and Potential energy in the phase field limit and that the associated varifold to the total energy converges to an integer rectifiable varifold with mean curvature in . The latter is a diffused version of Allard's convergence theorem for integer rectifiable varifolds.

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Source
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11525335PMC
http://dx.doi.org/10.1007/s00208-024-02909-6DOI Listing

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