A bound for the optimal constant in an inequality of Ladyzhenskaya and Solonnikov

Ladyzhenskaya & Solonnikov (1976) introduced a representationtheorem in ³, which contained an integral inequality involvinga multiplicative dimensionless constant. The existence of theconstant was established but not its magnitude which dependsonly on the shape of the domain. In this paper, we derive anupper bound for the optimal constant when the underlying domainis star shaped.