On a conjecture of De Giorgi related to homogenization

Aram Karakhanyan, Henrik Shahgholian

Research output: Working paper


For a periodic vector field F, let
Xϵ solve the dynamical system
In \cite{DeGiorgi} Ennio De Giorgi enquiers whether from the existence of the limit X0(t):=limϵ→0Xϵ(t) one can conclude that dX0dt=constant. Our main result settles this conjecture under fairly general assumptions on F, which may also depend on t-variable.
Once the above problem is solved, one can apply the result to the transport equation, in a standard way. This is also touched upon in the text to follow.
Original languageEnglish
Number of pages15
Publication statusPublished - 29 Dec 2015


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