Trudinger-Moser Inequalities with the Exact Growth Condition in ℝ^Nand Applications

Abstract

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Ground state solution for a class of indefinite variational problems with critical growth

“…The Trudinger-Moser inequalities will be strongly utilized throughout this section in order to deduce important estimates. The reader can find more recent results involving this inequality in [6], [10], [11], [18] and references therein…”

Improved Moser–Trudinger type inequalities in the hyperbolic spaceHn

“…The inequality (1.8) is sharp in the sense that if we replace α n by any constant α > α n or the power n n−1 in the denominator by any p < n n−1 then the supremum will be infinity. The Moser-Trudinger inequality with exact growth in Euclidean space R n was proved by Ibrahim, Masmoudi and Nakanishi [12] in the plane (i.e, n = 2) and by Masmoudi and Sani [32] for n ≥ 3. This inequality states that sup…”

“…It was also shown in [32] that the inequality (1.9) is sharp in the sense that if we replace α n by any constant α > α n or the power n n−1 in the denominator by any p < n n−1 then the supremum will be infinity. This kind of inequality was extended to the hyperbolic spaces by Lu and Tang [24] in the form sup…”

Singular Moser-Trudinger inequality with the exact growth condition on hyperbolic space

“… and obtained the Moser-Trudinger inequality in the whole space in the case of . Masmoudi and Sani in their elegant papers [23, 24] kept the two conditions and . They proved the following.…”