Sharp trace inequalities for fractional Laplacians
Amit Einav, Michael Loss
TL;DR
This paper extends the sharp trace inequality for the fractional Laplacian on R^n, providing a complete characterization of equality cases using Fourier analysis and Lieb's Hardy-Littlewood-Sobolev inequality.
Contribution
It generalizes Escobar's trace inequality to fractional Laplacians and characterizes all cases of equality.
Findings
Extended sharp trace inequality to fractional Laplacians
Characterized all equality cases for the inequality
Utilized Fourier transform and Lieb's inequality in proofs
Abstract
The sharp trace inequality of Jose Escobar is extended to traces for the fractional Laplacian on R^n and a complete characterization of cases of equality is discussed. The proof proceeds via Fourier transform and uses Lieb's sharp form of the Hardy-Littlewood-Sobolev inequality.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Advanced Harmonic Analysis Research