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scholarly journals MAXIMUM PRINCIPLES FOR SOME HIGHER-ORDER SEMILINEAR ELLIPTIC EQUATIONS

2010 ◽  
Vol 53 (2) ◽  
pp. 313-320 ◽  
Author(s):  
A. MARENO
Keyword(s):  
Elliptic Equations ◽  
Auxiliary Function ◽  
Higher Order ◽  
Semilinear Elliptic Equations ◽  
Maximum Principles ◽  
Eighth Order ◽  
Analyse Math ◽  
Semilinear Elliptic

AbstractWe deduce maximum principles for fourth-, sixth- and eighth-order elliptic equations by modifying an auxiliary function introduced by Payne (J. Analyse Math. 30 (1976), 421–433). Integral bounds on various gradients of the solutions of these equations are obtained.

Bounds for the best constant in Landau/s inequality on the line

1983 ◽  
Vol 95 (3-4) ◽  
pp. 257-262 ◽  
Author(s):  
Z. M. Franco ◽  
Hans G. Kaper ◽  
Man Kam Kwong ◽  
A. Zettl
Keyword(s):  
Lower Bounds ◽  
Real Line ◽  
Upper Bound ◽  
Upper And Lower Bounds ◽  
Analyse Math ◽  
Best Constant ◽  
The Real ◽  
Explicit Formulae

SynopsisExplicit formulae and numerical values for upper and lower bounds for the best constant in Landau/s inequality on the real line are given. For p > 3, the value of the upper bound is less than the value of the best constant conjectured by Gindler and Goldstein (J. Analyse Math. 28 (1975), 213–238).

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