The $ϵ$-entropy of some infinite dimensional compact ellipsoids and fractal dimension of attractors

We prove an estimation of the Kolmogorov $ϵ$-entropy in H of the unitary ball in the space V, where H is a Hilbert space and V is a Sobolev-like subspace of H. Then, by means of Zelik’s result [5], an estimate of the fractal dimension of the attractors of some nonlinear parabolic equations is established.