A class of second order dilation invariant inequalities
Paolo Caldiroli, Roberta Musina
TL;DR
This paper determines the optimal constants for a class of second order inequalities that remain invariant under dilation, involving weights based on the distance from the origin.
Contribution
It introduces a method to compute the best constants in second order dilation invariant inequalities with power weights.
Findings
Exact best constants are derived for the inequalities studied.
The results extend previous work on first order inequalities.
The inequalities have applications in analysis and PDEs.
Abstract
We compute the best constants in some second order dilation invariant inequalities, with weights being powers of the distance from the origin.
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Taxonomy
TopicsMathematical Inequalities and Applications · Analytic and geometric function theory · Fatigue and fracture mechanics