Data di Pubblicazione:
2017
Citazione:
Higher order Adams' inequality with the exact growth condition / N. Masmoudi, F. Sani. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - (2017 Sep 06), pp. 1750072.1-1750072.33. [Epub ahead of print] [10.1142/S0219199717500729]
Abstract:
Adams' inequality is the complete generalization of the TrudingerâMoser inequality to the case of Sobolev spaces involving higher order derivatives. The failure of the original form of the sharp inequality when the problem is considered on the whole space (Formula presented.) served as a motivation to investigate in the direction of a refined sharp inequality, the so-called Adams' inequality with the exact growth condition. Due to the difficulties arising in the higher order case from the lack of direct symmetrization techniques, this refined result is known to hold on first- and second-order Sobolev spaces only. We extend the validity of Adams' inequality with the exact growth to higher order Sobolev spaces.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Adams inequalities; best constants; Limiting Sobolev embeddings
Elenco autori:
N. Masmoudi, F. Sani
Link alla scheda completa: