A Sharp Trudinger-Moser Type Inequality for Unbounded Domains in Rn

By Yuxiang Li, Bernhard Ruf. 2006

134 citations recorded by the source corpus.

The Trudinger-Moser inequality states that for functions u ∈ H 1,n 0 (Ω) (Ω c Ρ n a bounded domain) with J Ω |∇u| n dx 2. Also, we prove that for Ω = R n the supremum of ∫ R n (e αn|u|n/(n-1) - 1) dx over all such functions is attained. The proof is based on a blow-up procedure.

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

View Paper: https://www.semanticscholar.org/paper/da9377b4fcf3fc7a8073ad97baefedb994aafae9

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In Applied Mathematics

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

In Computational Theory and Mathematics

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

In Mathematical Physics

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

Citations in the corpus

• A new approach to sharp Moser–Trudinger and Adams type inequalities: A rearrangement-free argument (2013, methodology): “The existence and non-existence of extremal functions for such inequalities on unbounded domains were investigated by Ruf [47], Li and Ruf [38] and Ishiwata [25].”
• Existence and multiplicity of solutions to equations of $N-$Laplacian type with critical exponential growth in $\mathbb{R}^{N}$ (2011, background): “lity was first proved by D. Cao in [11], and proved for N > 2 by Panda [29] and J.M. do O [15, 16] and Adachi and Tanaka [1]. Recently, Adimurthi and Yang generalized the above result of Li and Ruf [25] to get the following version of the singular Trudinger-Moser inequality (see [5]): Lemma 1.1. F”
• Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space (2011, methodology): “Ruf in the case N = 2 via symmetrization method and by Li-Ruf [26] in general dimensional case via the method of b l w-up analysis.”
• EXISTENCE OF NONTRIVIAL SOLUTIONS TO POLYHARMONIC EQUATIONS WITH SUBCRITICAL AND CRITICAL EXPONENTIAL GROWTH (2012, unknown): “Li and Ruf in R [31].”
• Sharp Moser–Trudinger inequalities on Riemannian manifolds with negative curvature (2015, unknown): “In the case of unbounded domains, Ruf [16] and Li-Ruf [11] obtained the following inequality: ∫ Rn ( exp(β0|u|n/(n−1)) − n−2∑ k=0 βk0 |u|kn/(n−1) k!”
• Best Constants for Moser-Trudinger Inequalities on High Dimensional Hyperbolic Spaces (2013, unknown): “Ruf [20] (for the general case n ≥ 2) established a critical Moser-Trudinger type inequality for unbounded domains in Euclidean spaces.”
• Sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs (2014, unknown): “In order to obtain a Moser–Trudinger type inequality including the critical case αn, Ruf [7] and Li–Ruf [8] used the full norm of the Sobolev space W 1,n (Rn), namely  ∥u∥n + ∥∇u∥ n n 1/n, instead of ∥∇u∥n, to set up the result in the critical case α = αn.”
• Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications ✩ (2012, methodology): “In this case, the sharp Moser–Trudinger type inequality was obtained in [65] in dimension two and in [53] in general dimension.”