Trudinger-Moser inequality with remainder terms

By C. Tintarev. 2012

90 citations recorded by the source corpus.

The paper gives an improvement of the Trudinger-Moser inequality, in which the constraint set is defined not by the squared gradient norm, but with the squared gradient norm minus a remainder term of the weighted L^p-type. This is a two-dimensional counterpart of the Hardy-Sobolev-Mazya inequality in higher dimensions, which is a similar refinement of the limiting Sobolev inequality. In particular, we generalize two known cases of remainder terms of potential type (i.e. weighted L^2-terms) found by Adimurthi and Druet and by Wang and Ye. In addition, we prove the inequality with a L^p-remainder, p>2, as well as give an analogous improvement for the Onofri-Beckner inequality.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/06a4c323da5e2f8cd58cd55a187444747bfaae08

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In Applied Mathematics

1. Xiaobao Zhu
2. Y. Yang
3. Giovanni Mancini
4. K. Sandeep
5. C. Tintarev
6. G. Lu
7. Nguyen Huong Lam
8. Caifeng Zhang

In Computational Theory and Mathematics

1. Xiaobao Zhu
2. Y. Yang
3. C. Tintarev
4. K. Sandeep
5. Giovanni Mancini
6. G. Lu
7. Nguyen Huong Lam
8. Caifeng Zhang

Citations in the corpus

• Extremal functions for Trudinger-Moser inequalities of Adimurthi-Druet type in dimension two (2015, background): “r-Moser inequality with interior singularity had been established by Adimurthi-Sandeep [2] on bounded smooth domain and Adimurthi and the author [4] on the whole Euclidean space. Moreover C. Tintarev [36] modified the classical Trudinger-Moser inequality as follows: LetΩ be a smooth bounded domain in”
• Trudinger–Moser inequality in the hyperbolic space ℍN (2013, background): “Versions of the Trudinger–Moser inequality with a remainder term related to the metric of the Poincaré ball were recently proved in [24, 26].”
• Blow-up analysis concerning singular Trudinger–Moser inequalities in dimension two (2016, background): “This result was extended by Y. Yang [28, 29] to the cases of high dimension and compact Riemannian surface, by Lu-Yang [19] and J. Zhu [38] to the version of Lp-norm, by de Souza and J. M. do Ó [11, 13] to the whole Euclidean space, and by Tintarev [25] to the following form sup u∈W1,2 0 (Ω), ‖u‖1,”