A sharp Trudinger-Moser type inequality for unbounded domains in R 2

By Bernhard Ruf. 2005

541 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fa3a801ce8c73a4ad70add8389dc2e7c68233c97

How researchers see this paper

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. Caifeng Zhang
4. Y. Yang
5. Federica Sani
6. Nader Masmoudi
7. Hanli Tang
8. Lu Zhang

In Computational Theory and Mathematics

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

In Geometry and Topology

1. Nguyen Huong Lam
2. G. Lu
3. Y. Yang
4. Federica Sani
5. Caifeng Zhang
6. Hanli Tang
7. C. Tintarev
8. J. M. do

Citations in the corpus

• Adams' inequalities for bi-Laplacian and extremal functions in dimension four (2009, unknown): “Li [21] and Yang [43], and by Lu and Yang [29] for functions with mean value zero, and on unbounded domains by Ruf in R2 [35].”
• Sharp singular Adams inequalities in high order Sobolev spaces (2011, result): “Our results extend the singular Moser-Trudinger inequalities of first order in [7, 46, 39, 11] to the higher order Sobolev spaces W n m and the results of [47] on Adams type inequalities in unbounded domains to singular case.”
• Equivalence of critical and subcritical sharp Trudinger-Moser-Adams inequalities (2015, methodology): “ble in many other non-Euclidean settings. The above inequality fails at the critical case α= αN. So it is natural to ask when the above can be true when α= αN. This is done by Ruf [21] and Li and Ruf [16] by using the restriction of the full norm of the Sobolev space W1,N RN : hR RN |∇u| N +τ R RN |”
• Sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs (2014, unknown): “[8] Y.X. Li, B. Ruf, A sharp Trudinger–Moser type inequality for unbounded domains in Rn , Indiana Univ. Math.”
• A nonhomogeneous elliptic problem involving critical growth in dimension two (2008, methodology): “Here we shall use the following extension of these results for the whole space R2 obtained by [9] (see also [13,21] for a more complete result).”
• On a version of Trudinger–Moser inequality with Möbius shift invariance (2009, background): “ef 2N N−2 , and it is unbounded on any bounded subset of H1(RN) when p > 2∗. In the case N = 2, the functional R R2 e pu2dx on the set {u ∈ H1(R2),kuk H1 ≤ 1} is bounded if and only if p ≤ 4π (see [12]). The analogy extends also to weak continuity properties. For obvious reason of translation inv”
• Trudinger-Moser inequality with remainder terms (2012, background): “When Ω = R2, inequality (0.1) with Q(u) = k∇uk2 2 is false, since the form k∇uk2 2 on the whole R 2 admits a ground state 1. On the other hand, the inequality holds when Q(u) = k∇uk2 2 + kuk2 2 (Ruf, [22]). Furthermore, according to the result announced in the thesis summary [10] of Gabriele Mancini”
• Elliptic Equations and Systems with Subcritical and Critical Exponential Growth Without the Ambrosetti–Rabinowitz Condition (2014, unknown): “In the case N = 2, motivated by the Moser–Trudinger inequality (see Lemma 3), existence of nontrivial solutions to problems of the above type when f has exponential growth has been studied by many authors; see, for example, Carleson–Chang [9], Atkinson–Peletier [6], Shaw [40], Adimurthi et al. [1] [”
• 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].”