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A DeGiorgi type conjecture for minimal solutions to a nonlinear Stokes equation

  • Radu Ignat (Université Paul Sabatier, Toulouse)
A3 01 (Sophus-Lie room)

Abstract

The aim is to study the symmetry of transition layers in Ginzburg-Landau type functionals for divergence-free maps in R^N. Namely, we determine a class of nonlinear potentials such that the minimal transition layers are one-dimensional.

In particular, this class includes in dimension N=2 the nonlinearities w^2 with w being an harmonic function or a solution to the wave equation, while in dimension N>2, this class contains a perturbation of the standard Ginzburg-Landau potential as well as potentials having N+1 wells with prescribed transition cost between the wells. For that, we develop a theory of calibrations for divergence-free maps in R^N(similar to the theory of entropies for the Aviles-Giga model when N=2).

This is a joint work with Antonin Monteil (Louvain, Belgium).

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

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