21世紀COEプログラム : 特異性から見た非線形構造の数学

H^∞ - calculus for the Stokes operator on L^q - spaces : J. Saal (Hokkaido Univ.)

After introducing the notion and the significance of a bounded H^∞-calculus for linear operators we will prove that the Stokes operator on L^q_σ(Ω) admits this property.

Here Ω is a domain in Rⁿ either bounded, exterior, or a perturbed half-space.

The starting point will be the result on the half-space. By using an abstract perturbation theorem, this result can be transfered to bent half-spaces.

The application of a localizaton procedure then will lead to the bounded H^∞-calculus for the Stokes operator on L^q_σ(Ω) for the mentioned domains Ω.

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