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

  • * Corresponding author: Alain Haraux

    * Corresponding author: Alain Haraux
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  • We prove an estimation of the Kolmogorov $\varepsilon$ -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 [7], an estimate of the fractal dimension of the attractors of some nonlinear parabolic equations is established.

    Mathematics Subject Classification: 37L30, 35B41.


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