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A cost on paths of measures which induces the Fokker-Planck equation.
No full textIn [12], Feng and Nguyen (2012) define a cost on curves of measures which is finite
exactly on the curves which solve a Fokker–Planck equation with L2 drift. In this
paper, using ideas of D. Gomes and E. Valdinoci, we give a different construction of
the cost of Feng and Nguyen (2012)
The stochastic value function in metric measure spaces
No full textLet be a compact metric space and let be a Borel probability measure on
. We shall prove that, if is a space, then the stochastic value function satisfies the viscous Hamilton-Jacobi equation, exactly as in Fleming's theorem on
Many solutions of elliptic problems on R^n of irrational slope
No full textWe consider the problem on , where is
a smooth function periodic of period 1 in all its variables. We show
that, under suitable hypotheses on , this
problem has a family of non self intersecting solutions
, which are at finite distance from a plane of slope
(\o,0,\dots,0) with \o irrational.
These solutions depend on a real parameter ;
if , then the closures of the integer translates of
and of do not intersect
The Aubry set for a version of the Vlasov equation.
Full text linkWe check that several properties of the Aubry set, first proven for finite-dimensional Lagrangians by Mather and Fathi, continue to hold in the ase of the infinitely many interacting particles of the Vlasov equation
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