Balls are Maximizers of the Riesz-Type Functionals with Supermodular Integrands
Hichem Hajaiej
TL;DR
This paper proves that for a broad class of supermodular integrands, the optimal shapes that maximize certain Riesz-type functionals under constraints are uniquely balls, up to translation.
Contribution
It establishes conditions under which balls are the unique maximizers of Riesz-type functionals with supermodular integrands, extending previous results.
Findings
Balls are the unique maximizers under specified conditions.
Conditions for maximization are explicitly characterized.
Results apply to a broad class of supermodular integrands.
Abstract
For a large class of supermodular integrands, we establish conditions under which balls are the unique (up to translations) maximizers of the Riesz-type functionals with constraints.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Approximation Theory and Sequence Spaces · Advanced Banach Space Theory