The Maximum Modulus Theorem

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.

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ON THE TRACTION PROBLEM FOR THE STOKES SYSTEM

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s021820250200191x ◽

2002 ◽

Vol 12 (06) ◽

pp. 813-834 ◽

Cited By ~ 11

Author(s):

GIULIO STARITA ◽

ALFONSINA TARTAGLIONE

Keyword(s):

Stokes System ◽

Existence Theorems ◽

Maximum Modulus ◽

Integral Representations ◽

Classical Solutions ◽

Maximum Modulus Theorem ◽

Class C

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.

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ON THE MAXIMUM MODULUS THEOREM IN LINEAR ELASTOSTATICS FOR EXTERIOR DOMAINS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202596000304 ◽

1996 ◽

Vol 06 (06) ◽

pp. 721-728

Author(s):

GIULIO STARITA

Keyword(s):

Positive Constant ◽

Three Dimensional ◽

Maximum Modulus ◽

Finite Energy ◽

Exterior Domains ◽

Dirichlet Data ◽

Maximum Value ◽

Linear Elastostatics ◽

Maximum Modulus Theorem

This paper deals with the system of linear elastostatics in exterior three-dimensional domains. We prove that the modulus of every solution with finite energy of such a system may be majorized by a positive constant times the maximum value of the modulus of the Dirichlet data at the boundary (maximum modulus theorem).

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