Inversion positivity and the sharp Hardy–Littlewood–Sobolev inequality
By Rupert L. Frank, Elliott H. Lieb. 2009
135 citations recorded by the source corpus.
We give a new proof of certain cases of the sharp HLS inequality. Instead of symmetric decreasing rearrangement it uses the reflection positivity of inversions in spheres. In doing this we extend a characterization of the minimizing functions due to Li and Zhu.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/a9f195f854af7c0d0788ef2baae8520bc0298129
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In Applied Mathematics
- Rupert L. Frank
- Yannick Sire
- Manuel del Pino
- J. D'avila
- Jingbo Dou
- Meijun Zhu
- Elliott H. Lieb
- Jun-cheng Wei
In Computational Theory and Mathematics
- Jingbo Dou
- Meijun Zhu
- Rupert L. Frank
- J. D'avila
- Yannick Sire
- Manuel del Pino
- Elliott H. Lieb
- Jun-cheng Wei
Citations in the corpus
- Nondegeneracy of the bubble in the critical case for nonlocal equations (2013, background): “[10] Rupert L. Frank and Elliott H. Lieb, Inversion positivity and the sharp Hardy-LittlewoodSobolev inequality, Calc.”
- ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR NONLINEAR ELLIPTIC PROBLEMS WITH THE FRACTIONAL LAPLACIAN (2013, unknown): “2) (refer to [23, 5, 15]).”
- A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality (2010, background): “Another proof, but only for N − 2 ≤ λ < N , was recently given in [10].”
- SHARP HARDY-LITTLEWOOD-SOBOLEV INEQUALITY ON THE UPPER HALF SPACE (2013, methodology): “See, for example, Brascamp, Lieb and Luttinger [3].”