Peter Sternberg

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math.AP2025

Local minimizers in $3$ d of vector Allen-Cahn with a quadruple junction

Abhishek Adimurthi, Peter Sternberg

For $I^c ◯$ a perturbation of the unit ball in $R^{3}$ , we establish the existence of a sequence of local minimizers for the vector Allen-Cahn energy. The sequence converges in…

math.AP2025

Minimizing solutions of degenerate Allen-Cahn equations with three wells in $R^{2}$

Lia Bronsard, Ãtienne Sandier, Peter Sternberg

We characterize all minimizers of the vector-valued Allen-Cahn equation in $R^{2}$ under the assumption that the potential $W$ has three wells and that the associated degene…

Local minimizers in 3d of vector Allen-Cahn with a quadruple junction

Minimizing solutions of degenerate Allen-Cahn equations with three wells in R2

Local minimizers in $3$ d of vector Allen-Cahn with a quadruple junction

Minimizing solutions of degenerate Allen-Cahn equations with three wells in $R^{2}$