There are considered classical solutions of the Stokes system in the ball , which are continuous up to the boundary. We derive the-optimal constant , such that, for all ,
holds for all such functions. We show that exists, where is the minimal constant in (*) for any fixed . The constants are determined explicitly via the Stokes-Poisson integral formula and via a general theorem on the norm of certain linear mappings given by some matrix kernel. Moreover, the asymptotic behaviour of the as and as is derived.
In the concluding section the general result on the norm of linear mappings is used to prove two inequalities: one for linear combinations of Fourier coefficients and the other from matrix analysis.
Cite this article
Werner Kratz, An Extremal Problem Related to the Maximum Modulus Theorem for Stokes Functions. Z. Anal. Anwend. 17 (1998), no. 3, pp. 599–613DOI 10.4171/ZAA/841