Maximum Modulus Theorem and Applications

2012 ◽  
pp. 103-125
Author(s):  
Graziano Gentili ◽  
Caterina Stoppato ◽  
Daniele C. Struppa
Keyword(s):  
Maximum Modulus ◽  
Maximum Modulus Theorem

scholarly journals Some Inequalities for the Maximum Modulus of Rational Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-4
Author(s):  
Robert Gardner ◽  
Narendra Kumar Govil ◽  
Prasanna Kumar
Keyword(s):  
Maximum Modulus ◽  
Rational Functions ◽  
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.

ON THE TRACTION PROBLEM FOR THE STOKES SYSTEM

2002 ◽  
Vol 12 (06) ◽  
pp. 813-834 ◽  
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.

ON THE MAXIMUM MODULUS THEOREM IN LINEAR ELASTOSTATICS FOR EXTERIOR DOMAINS

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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