Note on Friedrichs' inequality in \(N\)-star-shaped domains (Q898870)

The authors establish an explicit constant in the Friedrichs inequality (also called Poincaré or Friedrichs-Poincaré inequality). They obtain two generalizations. The first one is for the so-called \(N\)-star-shaped domains (which can be written as union of \(N\)-domains star-shaped with respect to convex sets). The second generalization uses higher-order moments when replacing the integral mean of the function by the mean of higher-order Taylor polynomials. The results are too complicated to be stated here.