Moser-Trudinger inequality on conformal discs
56 citations recorded by the source corpus.
We show that the Moser-Trudinger inequality holds in a conformal disc if and only if the metric is bounded from above by the Hyperbolic metric. We also find a necessary and sufficient condition for the Moser-Trudinger inequality to hold in an unbounded subset of the two dimensional Euclidean space.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/d2b765f18ee2eeacd24af9b31046eb78f7fcd8c6
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- A sharp Trudinger–Moser inequality on any bounded and convex planar domain (2015, background): “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 1,20 (B), ∫ B |∇u|2dxdy≤1 ∫ B e4πu 2 − 1 (1− |z|2)2dxdy ∞.”
- 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: sup u∈C∞0 (B2), ∫ B2 |∇u|2dx≤1 ∫ B2 e4πu 2 − 1 (1 − |x |2)2 dx ∞, (1.4) where B2 is the unit ball at origin of R2.”
- 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]:”
- Fractional Adams–Moser–Trudinger type inequalities (2015, background): “An interesting question in whether fractional Adams-Moser-Trudinger inequalities hold for some domains of infinite measure, in the spirit of the results of Gianni Mancini-Sandeep [34] and Battaglia-Gabriele Mancini [6] who in dimension 2 and in the classical case p = 2 proved that the inequality sup”
- A new approach to sharp Moser–Trudinger and Adams type inequalities: A rearrangement-free argument (2013, background): “There are also other improved Moser–Trudinger inequalities on the unit disk in R2, which was recently proved and studied in [4,44]:”