Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications ✩

By Nguyen Huong Lam, G. Lu. 2012

159 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e6004e101c7c85a96995a5f668875a9fcb1282fb

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In Applied Mathematics

1. G. Lu
2. Nguyen Huong Lam
3. Hanli Tang
4. Qiaohua Yang
5. Jiuyi Zhu
6. Caifeng Zhang
7. Y. Yang
8. Wenxiong CHEN *

In Computational Theory and Mathematics

1. G. Lu
2. Nguyen Huong Lam
3. Hanli Tang
4. Jiuyi Zhu
5. Qiaohua Yang
6. Caifeng Zhang
7. Y. Yang
8. Federica Sani

Citations in the corpus

• Sharp singular Adams inequalities in high order Sobolev spaces (2011, methodology): “We should mention that using the rearrangement-free argument developed in [33], we have proved in [36] sharp subcritical Moser-Trudinger type inequalities on the Heisenberg group and sharp Moser-Trudinger inequality on the Heisenberg group with full norm in [34].”
• Hardy–Littlewood–Sobolev and Stein–Weiss inequalities and integral systems on the Heisenberg group (2012, unknown): “Recently, Lam and the second author have established in [15] the sharp Moser–Trudinger inequality on the whole Heisenberg group: There exists a positive constant α Q = Q  2π n Γ ( 1 2 )Γ ( Q −1 2 ) Γ (Q 2)Γ (n)  Q ′ −1 such that for any pair β and α satisfying 0 ≤ β < Q , 0 < α ≤ α Q (1 −”
• N-Laplacian Equations in ℝN with Subcritical and Critical GrowthWithout the Ambrosetti-Rabinowitz Condition (2013, methodology): “Subelliptic equations of exponential growth on the Heisenberg group have also been studied recently in [12], [29] and [30] using the sharp Moser-Trudinger inequality on domains of finite measure proved in [11] and its analogue on unbounded domains.”
• Sharp Singular Trudinger–Moser Inequalities in Lorentz–Sobolev Spaces (2016, methodology): “Such critical Trudinger–Moser inequalities on unbounded domains on the Heisenberg group have been established by Lam and Lu [19] where symmetrization is not available.”
• A new approach to sharp Moser–Trudinger and Adams type inequalities: A rearrangement-free argument (2013, methodology): “Our approach can be applied to other non-Euclidean settings where the symmetrization does not hold (see for example on the Heisenberg group, [30]).”
• Improved Moser-Trudinger Inequality Involving Lp Norm in n Dimensions (2014, background): “We refer the reader to [4], [5], [7], [8], [9], [20], etc.”
• Sharp Moser–Trudinger inequalities on Riemannian manifolds with negative curvature (2015, background): “2 follows closely LamandLu’s proof (see [8], section 2 or [9], section 5).”
• Sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs (2014, unknown): “With this new method, we can set up the following sharp Moser–Trudinger type inequality on unbounded domain in [16]: Theorem E.”