Adams' inequalities for bi-Laplacian and extremal functions in dimension four
100 citations recorded by the source corpus.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/3a0cc980e948a788135c904d794b8d37a5b540ab
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In Applied Mathematics
In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- 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.”
- A new approach to sharp Moser–Trudinger and Adams type inequalities: A rearrangement-free argument (2013, background): “We also mention whether Adams inequality has an extremal function is still open except for the case n = 2m = 4 and Ω ⊂ R4 is a smooth oriented bounded domain that is studied by Lu and Yang in [42] and on compact Riemannian manifolds without boundary of dimension four by Y.”
- Sharp Adams type inequalities in Sobolev spaces Wm,nm(Rn) for arbitrary integer m (2012, background): “[8] Adimurthi, Y. Yang, An interpolation of Hardy inequality and Trudinger–Moser inequality in RN and its applications, Int.”
- Sharp Adams-type inequalities in ℝⁿ (2012, methodology): “In the case m = 2 and n = 4, we will consider a sequence of test functions that was used in [15] to prove a generalized version of Adams’ inequality for bounded domains in R.”
- Adams' Inequality with the Exact Growth Condition in ℝ4 (2014, background): “R(4)/ with kuk2 1: We consider the sequence of test functions fukgk 1 introduced in [28]:”
- EXISTENCE OF NONTRIVIAL SOLUTIONS TO POLYHARMONIC EQUATIONS WITH SUBCRITICAL AND CRITICAL EXPONENTIAL GROWTH (2012, background): “In the particularly interesting case n = 4 and m = 2, β(4, 2) = 32π(2) and the existence of the extremal function has been established in [30], [34].”
- Adams type inequalities and related elliptic partial differential equations in dimension four (2011, methodology): “Secondly, forα > 32π2, we employ a sequence of functions uǫ constructed in Section 2 of [25] (see also (33) in [32]).”
- A Hardy-Moser-Trudinger inequality (2010, background): “A generalization of (4) to a higher dimensional ball like in [24] and to higher order derivatives like in [1, 6, 17, 25] would be very interesting.”
- Sharp constant and extremal function for the improvedMoser-Trudinger inequality involving $L^p$ norm in two dimension (2009, background): “AN IMPROVED MOSER-TRUDINGER INEQUALITY 965 authors of the current paper derived in [19] the sharpened Adams inequalities for bi-Laplacian and extremal functions in dimension four, and existence of extremal function for Moser-Trudinger inequality for functions with mean value zero in R(2) in [20].”
- Equivalence of critical and subcritical sharp Trudinger-Moser-Adams inequalities (2015, background): “Existence of extremal functions for the Adams inequality on bounded domains in Euclidean spaces has been established in [18] and compact Riemannian manifolds by [14] only when N = 4 and m = 2 and is still widely open in other cases.”
- Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications ✩ (2012, background): “We also mention that existence of extremal functions for Adams inequalities has only been proved in dimension four (see [52,60]).”
- Sharp singular Adams inequalities in high order Sobolev spaces (2011, background): “We remark that we have also established in [37] sharp affine Moser-Trudinger inequalities and improved Moser-Trudinger-Adams inequalities in the spirit of [38], [5], [40].”