Ricerc@Sapienza

This paper is concerned with eigenvalue problems for elliptic operators with large drifts in bounded domains under Dirichlet boundary conditions. We consider the minimal principal eigenvalue and the related principal eigenfunction in the class of drifts having a given, but large, pointwise upper bound. We show that, in the asymptotic limit of large drifts, the maximal points of the optimal principal eigenfunctions converge to the set of points maximizing the distance to the boundary of the domain.

We study a Stokes problem in a three dimensional fractal domain
of Koch type and in the corresponding prefractal approximating domains. We
prove that the prefractal solutions do converge to the limit fractal one in a
suitable sense. Namely the approximating velocity vector elds as well as the
approximating associated pressures converge to the limit fractal ones respec-
tively.