The optimal Leray-Trudinger inequality
Giuseppina Di Blasio, Giovanni Pisante, Georgios Psaradakis
TL;DR
This paper determines the precise logarithmic correction exponent needed for the Leray-Trudinger inequality to hold, using spherical harmonics expansion instead of previous representation formulas.
Contribution
It provides the exact minimal exponent for the logarithmic correction in the Leray-Trudinger inequality, filling a gap in prior research.
Findings
Identifies the minimal logarithmic correction exponent for the inequality.
Employs spherical harmonics expansion as a novel proof technique.
Completes the theoretical understanding of the inequality's conditions.
Abstract
We fill the gap left open in \cite{MT}, regarding the minimum exponent on the logarithmic correction weight so that the Leray-Trudinger inequality (see \cite{PsSp}) holds. Instead of the representation formula used in \cite{PsSp} and \cite{MT}, our proof uses expansion in spherical harmonics as in \cite{VzZ}.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Numerical methods in inverse problems · Medical Imaging Techniques and Applications