Author:
Sun Xiaomei,Yu Kaixiang,Zhu Anqiang
Abstract
In this paper, we establish an infinite series expansion of Leray–Trudinger inequality, which is closely related with Hardy inequality and Moser Trudinger inequality. Our result extends early results obtained by Mallick and Tintarev [A. Mallick and C. Tintarev. An improved Leray-Trudinger inequality. Commun. Contemp. Math. 20 (2018), 17501034. OP 21] to the case with many logs. It should be pointed out that our result is about series expansion of Hardy inequality under the case
$p=n$
, which case is not considered by Gkikas and Psaradakis in [K. T. Gkikas and G. Psaradakis. Optimal non-homogeneous improvements for the series expansion of Hardy's inequality. Commun. Contemp. Math. doi:10.1142/S0219199721500310]. However, we can't obtain the optimal form by our method.
Publisher
Cambridge University Press (CUP)
Reference24 articles.
1. An improved Leray–Trudinger inequality
2. 20 Opic, B. and Kufner, A. , Hardy-type inequalities, Pitman Research Notes in Mathematics series, Volume 219 (Longman Scientific and Technical, Harlow, 1990).
3. Existence and non-existence of the first eigenvalue of the perturbed Hardy–Sobolev operator
4. Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique;Leray;J. Math. Pures Appl,1933
5. Elliptic Partial Differential Equations of Second Order