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The De Giorgi conjecture for the half-Laplacian in dimension 4

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If you have a question about this talk, please contact Mikaela Iacobelli .

The famous the Giorgi conjecture for the Allen-Cahn equation states that global monotone solutions are 1D if the dimension is less than 9. This conjecture is motivated by classical results about the structure of global minimal surfaces. The analogue of this conjecture in half-spaces can be reduced to study the problem in the whole space for the Allen-Cahn equation with the half-Laplacian. In this talk I will present a recent result with Joaquim Serra, where we prove the validity of the De Giorgi conjecture for stable solutions in dimension 3, that implies the result on monotone solutions in dimension 4.

This talk is part of the Geometric Analysis & Partial Differential Equations seminar series.

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