Some Inequalities for the Maximum Modulus of Rational Functions

For a polynomial p z of degree n , it follows from the maximum modulus theorem that max z = R ≥ 1 p z ≤ R n max z = 1 p z . It was shown by Ankeny and Rivlin that if p z ≠ 0 for z < 1 , then max z = R ≥ 1 p z ≤ R n + 1 / 2 max z = 1 p z . In 1998, Govil and Mohapatra extended the above two inequalities to rational functions, and in this paper, we study the refinements of these results of Govil and Mohapatra.

ON THE TRACTION PROBLEM FOR THE STOKES SYSTEM

The traction problem for the Stokes system is studied in the framework of the theory of the hydrodynamical potentials. Existence theorems and integral representations of classical solutions are given for domains having not connected boundary of class C1,α in both the bounded and exterior cases. Finally, a maximum modulus theorem is derived for the traction field in the direction of the normal to the boundary.

ON THE STOKES EQUATIONS: THE MAXIMUM MODULUS THEOREM

We consider the boundary value problem for classical solutions to the Stokes equations. We prove the existence, uniqueness and continuous dependence on the boundary data, which are assumed to be continuous only.