Asymptotics for vectorial Allen–Cahn type problems
Journées équations aux dérivées partielles (2023), Exposé no. 1, 16 p.
Voir la notice de l'acte provenant de la source Numdam
These notes present some recent results concerning the convergence of solutions to the elliptic vectorial Allen–Cahn equation in dimension two as the parameter 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.
@incollection{JEDP_2023____A1_0,
author = {Bethuel, Fabrice},
title = {Asymptotics for vectorial {Allen{\textendash}Cahn} type problems},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
note = {talk:1},
pages = {1--16},
publisher = {R\'eseau th\'ematique AEDP du CNRS},
year = {2023},
doi = {10.5802/jedp.672},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/jedp.672/}
}
TY - JOUR AU - Bethuel, Fabrice TI - Asymptotics for vectorial Allen–Cahn type problems JO - Journées équations aux dérivées partielles N1 - talk:1 PY - 2023 SP - 1 EP - 16 PB - Réseau thématique AEDP du CNRS UR - http://geodesic.mathdoc.fr/articles/10.5802/jedp.672/ DO - 10.5802/jedp.672 LA - en ID - JEDP_2023____A1_0 ER -
%0 Journal Article %A Bethuel, Fabrice %T Asymptotics for vectorial Allen–Cahn type problems %J Journées équations aux dérivées partielles %Z talk:1 %D 2023 %P 1-16 %I Réseau thématique AEDP du CNRS %U http://geodesic.mathdoc.fr/articles/10.5802/jedp.672/ %R 10.5802/jedp.672 %G en %F JEDP_2023____A1_0
Bethuel, Fabrice. Asymptotics for vectorial Allen–Cahn type problems. Journées équations aux dérivées partielles (2023), Exposé no. 1, 16 p.. doi: 10.5802/jedp.672
Cité par Sources :