An Interpolation of Hardy Inequality and Trudinger–Moser Inequality in ℝN and Its Applications

By Adimurthi, Y. Yang. 2009

247 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1468f86f34274170ecb528feaa2d5ef6e2a59e46

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Sharp singular Adams inequalities in high order Sobolev spaces (2011, background): “We refer the interested reader to [13], [16], [3], [7], [6], [9], [11], [8], [20], [21], [19], [27, 28], [49], [50] and the references therein.”
Yamabe type equations on graphs (2016, background): “For related works, we refer the reader to [10,2,25,26] and the references there in.”
Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications ✩ (2012, background): “Now, similarly as in the Euclidean case (see [6,24,40]), we have the following lemma.”
Trudinger–Moser Inequalities in Fractional Sobolev–Slobodeckij Spaces and Multiplicity of Weak Solutions to the Fractional-Laplacian Equation (2018, methodology): “Motivated by [3, 17, 27, 35, 63], we derive an application of Theorem 1.”
Sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs (2014, unknown): “These results were generalized recently in [9] where they proved that for all α ≤  1 − βn  αn and τ > 0,”
Sharp Adams-type inequalities in ℝⁿ (2012, unknown): “Yang [2] proved an analogous inequality in R involving critical Trudinger-Moser nonlinearities with singular Hardy coefficients.”
Trudinger-Moser Inequalities with the Exact Growth Condition in ℝ N and Applications (2015, background): “The authors of [4, 5, 13, 14, 16, 17, 20, 30], considering a potential V satisfying (1.”
Existence and multiplicity of solutions to equations of $N-$Laplacian type with critical exponential growth in $\mathbb{R}^{N}$ (2011, methodology): “Our existence result extends that in [5] to the nonuniformly elliptic type of equations.”
A new approach to sharp Moser–Trudinger and Adams type inequalities: A rearrangement-free argument (2013, methodology): “We also refer the reader to the sharp Moser inequality with mean value zero by Chang and Yang [11], Lu and Yang [43], Leckband [34], sharp Moser–Trudinger trace inequalities and sharp Moser–Trudinger inequalities without boundary conditions by Cianchi [12,13], the sharp Moser–Trudinger type inequali”
N-Laplacian Equations in ℝN with Subcritical and Critical GrowthWithout the Ambrosetti-Rabinowitz Condition (2013, unknown): “In the Euclidean spaces, see for example, [1], [2], [3], [8], [5], [7], [18], [19], [15], [16], [32], [31], [25], [26], [27], [28], [39], [40], etc.”
Equivalent Moser type inequalities in R2 and the zero mass case (2014, background): “Recently, a lot of attention has been given to Trudinger-Moser inequalities whose validity extends to the whole space, see [43, 22, 4, 36, 51, 35, 46, 47, 42, 37], and this is motivated by connections with mean field equations and conformal geometry [15, 16], two dimensional nonlinear Schrödinger an”
Best Constants for Moser-Trudinger Inequalities on High Dimensional Hyperbolic Spaces (2013, unknown): “It was extended further in [4] to the singular Moser-Trudinger type inequality on unbounded domains in Euclidean spaces.”