A sharp form of Moser–Trudinger inequality in high dimension
By Y. Yang. 2006
113 citations recorded by the source corpus.
Let Ω be a bounded smooth domain in Rn (n⩾3). This paper deals with a sharp form of Moser–Trudinger inequality. Let λ1(Ω)=infu∈H01,n(Ω),u≢0‖∇u‖nn/‖u‖nn be the first eigenvalue associated with n-Laplacian. Using blowing up analysis, the author proves that supu∈H01,n(Ω),‖∇u‖n=1∫Ωeαn(1+α‖u‖nn)1n−1|u|nn−1dx is finite for any 0⩽α<λ1(Ω), and the supremum is infinity for any α⩾λ1(Ω), where αn=nωn−11/(n−1), ωn−1 is the surface area of the unit ball in Rn. Furthermore, the supremum is attained for any 0⩽α<λ1(Ω).
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1a629ce3972df578fae1f224f6b17357f3fa5e79
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Blow-up analysis concerning singular Trudinger–Moser inequalities in dimension two (2016, background): “Yang [28, 29] to the cases of high dimension and compact Riemannian surface, by Lu-Yang [19] and J.”
- Improved Moser-Trudinger Inequality Involving Lp Norm in n Dimensions (2014, unknown): “The above two lemmas are similar to those in [11] and [24].”
- Extremal functions for Trudinger-Moser inequalities of Adimurthi-Druet type in dimension two (2015, methodology): “For earlier works involving this method, we refer the reader to [23, 40, 24, 26, 38].”
- Sharp constant and extremal function for the improvedMoser-Trudinger inequality involving $L^p$ norm in two dimension (2009, result): “Since the test function chosen in [1] does not meet our needs when p 6= 2, we will select a test function in our work which is quite different from that of [1], but more similar to that in [27].”