Asymptotics for vectorial Allen–Cahn type problems
Fabrice Bethuel1
1 Laboratoire Jacques-Louis Lions Sorbonne Université 4 place Jussieu 75252 Paris Cedex 5 France
Journées équations aux dérivées partielles (2023), Talk no. 1, 16 p.

These notes present some recent results concerning the convergence of solutions to the elliptic vectorial Allen–Cahn equation in dimension two as the parameter ε tends to zero, and its connections to minimal surface theory in the weak sense of stationary varifolds. We first describe the results obtained so far in the scalar theory, which can be considered as quite satisfactory, and provide some ideas about the proofs and their main steps. We then present some adaptations necessary to handle the vectorial case in dimension two.

Published online:
DOI: 10.5802/jedp.672
Fabrice Bethuel 1

1 Laboratoire Jacques-Louis Lions Sorbonne Université 4 place Jussieu 75252 Paris Cedex 5 France 
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Fabrice Bethuel. Asymptotics for vectorial Allen–Cahn type problems. Journées équations aux dérivées partielles (2023), Talk no. 1, 16 p. doi : 10.5802/jedp.672. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.672/

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