On the Planar Triple Junction Problem Without Symmetry Hypotheses
Time: 2022-11-07
Published By: Wenqiong Li
Speaker(s): Zhiyuan Geng (Basque Center for Applied Mathematics)
Time: 15:00-16:00 November 23, 2022
Venue: Online
For the scalar two-phase (elliptic) Allen-Cahn equation, there is a rich literature on a celebrated conjecture of De-Giorgi, which establishes the relationship of the diffuse interface with minimal surfaces. On the other hand, for three or more equally preferred phases, a vector order parameter is required. The structure of the diffuse interface is analogous to a singular minimal cone. These solutions are studied mostly in the presence of symmetry, but not at all in the general case.
In this talk, I will present some joint work with Nicholas Alikakos on the Allen-Cahn equation with a triple-well potential. We construct a minimizing solution that possesses a weak triple junction structure. The location and size of the diffuse interface are estimated from a tight energy upper/lower bound. We do not impose any symmetry hypothesis on the solution and we do not employ Gamma-convergence techniques.
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ID：533-624-586
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