Best constants for Moser-Trudinger inequalities on the Heisenberg group

By W. Cohn, G. Lu. 2001

174 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/58fd854d985ea55b291d3b4587fb6a3dff690456

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. G. Lu
2. Nguyen Huong Lam
3. Y. Yang
4. Caifeng Zhang
5. W. Cohn
6. Yuxiang Li
7. Hanli Tang
8. Federica Sani

In Computational Theory and Mathematics

1. G. Lu
2. Nguyen Huong Lam
3. Y. Yang
4. Caifeng Zhang
5. W. Cohn
6. Yuxiang Li
7. Hanli Tang
8. Federica Sani

In Mathematical Physics

1. G. Lu
2. Nguyen Huong Lam
3. Y. Yang
4. W. Cohn
5. Yuxiang Li
6. Hanli Tang
7. Jiuyi Zhu
8. Xiaobao Zhu

Citations in the corpus

• Adams' inequalities for bi-Laplacian and extremal functions in dimension four (2009, unknown): “This idea has also been developed to derive the sharp constants for Adams’ inequality involving higher order derivatives on Riemannian manifolds without boundary by Fontana [17] and more recently in the subelliptic setting to derive the sharp Moser’s inequality on the Heisenberg group and CR sphere ”
• An asymmetric affine Pólya–Szegö principle (2012, unknown): “, [4,17,18,24,32,45,63]).”
• A new approach to sharp Moser–Trudinger and Adams type inequalities: A rearrangement-free argument (2013, methodology): “We note the Moser–Trudinger inequality on domains of finite measure in the Carnot group was given in [6] which extends the results on the Heisenberg group and groups of Heisenberg type in [14,16].”
• Best Constants for Moser-Trudinger Inequalities on High Dimensional Hyperbolic Spaces (2013, unknown): “in [14], [18] which improve the earlier work on bounded domains by Cohn and Lu [9, 10] (see also [17]) or for Adams inequalities [2] on high (fractional) order Sobolev spaces by Lam and Lu in [15], [16] which improve the work of Ruf and Sani [25].”
• Sharp constants for Moser‐Trudinger inequalities on spheres in complex space ℂn (2004, methodology): “Motivated by [17], the prominent role of the Heisenberg group H and the sphere in C in CR geometry, and the intimate relationship between them (see expositions for such a relationship in [16, 37]), in this paper we investigate the sharp Moser-Trudinger and Moser-Onofri inequalities on the sphere in ”
• Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications ✩ (2012, background): “3 was extended to the groups of Heisenberg type in [20] and to general stratified groups in [8].”
• Sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs (2014, unknown): “Using similar ideas of [11], we considered in [14] the sharp singular Moser–Trudinger inequality on bounded domains in the Heisenberg group H.”
• Improved Moser-Trudinger Inequality Involving Lp Norm in n Dimensions (2014, unknown): “We refer the reader to [4], [5], [7], [8], [9], [20], etc.”
• A Moser-Trudinger inequality on the boundary of a compact Riemann surface (2005, background): “Especially, the sharp constants play an essential role as they contain geometry and probabilistic information, which have been already evidenced by many works ([6], [8], [ 9 ], [10], [11], [27], [28], [31]).”
• Sharp Singular Trudinger–Moser Inequalities in Lorentz–Sobolev Spaces (2016, unknown): “, see [5, 13, 14, 22] and [16, 26, 27], respectively.”
• 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.”