Sharp Constants for Inequalities of Poincar\'e Type: An Application of Optimal Control Theory
Hongwei Lou
TL;DR
This paper determines the best possible constants in Poincaré-type inequalities using optimal control theory, providing precise bounds that improve understanding of these fundamental inequalities.
Contribution
It introduces a novel application of optimal control theory to find sharp constants in Poincaré-type inequalities, advancing mathematical analysis techniques.
Findings
Derived explicit sharp constants for Poincaré inequalities
Demonstrated the effectiveness of optimal control methods in inequality analysis
Provided a framework for future research in inequality optimization
Abstract
Sharp constants for an inequality of Poincar\'e type is studied. The problem is solved by using optimal control theory.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Quantum chaos and dynamical systems · Functional Equations Stability Results