On a version of Trudinger–Moser inequality with Möbius shift invariance
By Adimurthi, Kyril Tintarev. 2009
48 citations recorded by the source corpus.
The paper raises a question about the optimal critical nonlinearity for the Sobolev space in two dimensions, connected to loss of compactness, and discusses the pertinent concentration compactness framework. We study properties of the improved version of the Trudinger–Moser inequality on the open unit disk $${B\subset\mathbb R^2}$$, recently proved by Mancini and Sandeep [g], (Arxiv 0910.0971). Unlike the original Trudinger–Moser inequality, this inequality is invariant with respect to the Möbius automorphisms of the unit disk, and as such is a closer analogy of the critical nonlinearity $${\int |u|^{2^*}}$$ in the higher dimension than the original Trudinger–Moser nonlinearity.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/ff8fd9b1629c3e881d15301df8a96b88bb2e5aef
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- Sharp Moser–Trudinger inequalities on Riemannian manifolds with negative curvature (2015, background): “Furthermore, if M is the hyperbolic space H2, Mancini and Sandeep [12] (see also [2]) proved the following inequality on H2:”
- A sharp Trudinger–Moser inequality on any bounded and convex planar domain (2015, unknown): “For instance, Mancini and Sandeep [14] (see also [3]) proved the following improved Trudinger-Moser inequalities on B = {z = x+ iy : |z| = √ x2 + y2 < 1}: sup u∈W 1,2 0 (B), ∫ B |∇u|2dxdy≤1 ∫”
- Sharp singular Adams inequalities in high order Sobolev spaces (2011, background): “There is another improved Moser-Trudinger inequality on the disk B ⊂ R(2), which was recently proved and studied in [10, 41]:”
- A Hardy-Moser-Trudinger inequality (2010, background): “eorem 1, since H(u) ≤ Hd(u) for any u ∈ C∞ 0 (B). A HARDY-MOSER-TRUDINGER INEQUALITY 3 There is another improved Moser-Trudinger inequality on the disc in R2, which was recently proved and studied in [24, 4]. sup u∈H1 0(B),k∇uk2≤1 Z B e4πu2 −1 (1 −|x|2)2 (6) dx < ∞. For other generalizations of t”
- Moser-Trudinger inequality on conformal discs (2009, background): “After a personal communication,in [3] the inequality (1.”
- Trudinger-Moser inequality with remainder terms (2012, background): “ty (1.2) is also false if the nonlinearity |u|2∗ is multiplied by an unbounded radial monotone function, although (1.1) on the unit disk holds also when the integrand is replaced by e4πu 2 −1 (1−r)2 ([4, 12]). This paper studies another refinement of (1.1), whose analogy in the case N ≥ 3 is the Mazy”