Trudinger type inequalities in R^N and their best exponents

By Shinji Adachi, Kazunaga Tanaka. 2000

277 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/dd1f7d364c6fa6c4cfe46cf459bd495865b45e5f

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Citations in the corpus

Sharp Singular Trudinger–Moser Inequalities in Lorentz–Sobolev Spaces (2016, methodology): “Surprisingly, Lam, Lu and Zhang [24] have shown that the subcritical Moser–Trudinger inequality in [1] and the critical Trudinger–Moser inequality in [28, 36] are actually equivalent.”
Best Constants for Moser-Trudinger Inequalities on High Dimensional Hyperbolic Spaces (2013, unknown): “Next, we will prove the following sharp singular Adachi-Tanaka type inequality on the entire hyperbolic space which extends the result of Theorem 1.2.”
Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space (2011, result): “A similar but different type inequality was obtained by Adachi and Tanaka [1].”
Existence and concentration of ground state solutions for a critical nonlocal Schrödinger equation in R2 (2016, background): “The first version of the Pohozaev-Trundiger-Moser inequality in R2 was established by Cao in [12], see also [41, 2, 13], and reads as follows Trudinger-Moser Lemma 1.”
Adams type inequalities and related elliptic partial differential equations in dimension four (2011, background): “Later Adachi and Tanaka [1] gave another type of generalization.”
Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications ✩ (2012, methodology): “Therefore, the argument in [1] does not work on H.”
A new approach to sharp Moser–Trudinger and Adams type inequalities: A rearrangement-free argument (2013, background): “There are also attempts to extend the Moser–Trudinger inequality to unbounded domains while only restricting the norm ∫ Rn |∇u|n dx instead of ‖u‖1,τ , namely, by D. Cao [9] in dimension two and by Adachi and Tanaka [1] in high dimension.”
Sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs (2014, unknown): “We note here that our proof of Theorem 1.2 (and hence Theorem 1.1) does not rely on the method of symmetrization which was used by Adachi–Tanaka in [6] on the Euclidean space.”
A sharp Trudinger-Moser type inequality for unbounded domains in R 2 (2005, background): “unbounded domains have been proposed by Cao [5] and Tanaka [2], however they assume a growth eαu 2 with α < 4π, i.”