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D'Atri Memorial Lectures

The De Giorgi Conjecture for the Half-Laplacian in Dimension 4 Part II

Alessio Figalli - ETH ZURICH

Date & time: Wednesday, 06 February 2019 at 10:30AM - 11:30AM

ABSTRACT: The famous De 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 the study of the problem in the whole space for the Allen-Cahn equation with the half-Laplacian. In these lectures I will first give a general overview of the problem and then 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.

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