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Junior Analysis
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Daniel E Restrepo, : Stability estimates for an isoperimetric problem involving the Allen-Cahn equation
Friday, March 05, 2021, 11:00am - 12:00pm
The classical results of Modica and Mortola show that the minimizers of the Allen-Cahn energy converge to minimizers of the area functional, under certain assumptions. In this talk, we will start exploring how this result can be extended for the case of the classical isoperimetric problem. In the first part of the talk, we will discuss briefly the properties of the solutions of this functional isoperimetric problem: existence, uniqueness, regularity and convergence. In the second part, we will present global and local stability estimates for these solutions (estimates for the distance of almost minimizer to the minimizer in terms of their difference in energy) , recovering the classical results for the isoperimetric problem as the limiting case.

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