WebFeb 15, 2005 · The classical Trudinger–Moser inequality says that for functions with Dirichlet norm smaller or equal to 1 in the Sobolev space H 0 1 ( Ω) (with Ω ⊂ R 2 a bounded domain), the integral ∫ Ω e 4 π u 2 dx is uniformly bounded by a constant depending only on Ω. If the volume Ω becomes unbounded then this bound tends to infinity, and ... WebDec 25, 2024 · The classical Moser-Trudinger inequality in the real two dimensional space was obtained by Trudinger [22] and Moser [17]. Let Ω be a bounded domain in R 2 . Then …

Blow-up analysis concerning singular Trudinger-Moser inequalities …

WebApr 10, 2024 · The proof is based on constrained variational method, fractional Trudinger–Moser inequality, quantitative deformation lemma and Brouwer's degree theory in Nehari sets. To be more precise, the ... WebFeb 18, 2014 · The classical Trudinger-Moser inequality [ 1 – 3] says for some constant depending only on , where is the usual Sobolev space and denotes the Lebesgue measure of . In the case where is an unbounded domain of , the above integral is infinite, but it was shown by Cao [ 4 ], Panda [ 5 ], and do Ó [ 6] that for any and any there holds Later Ruf ... examples of a bio for work

On the existence of an extremal function for an inequality of (1986)

WebJul 1, 2015 · Trudinger–Moser inequalities on manifolds, see L. Fontana [13] – Improvements and sharpening of Moser’s inequality: Adimurthi–Druet [2], and Masmoudi–Sani [22] – Moser inequalities with other boundary conditions, see Cianchi [9] – Extension of the Trudinger–Moser inequality to higher order Sobolev spaces: Adams [1], … WebWe establish an interpolation of Hardy inequality and Trudinger–Moser inequality in ℝ N (N ≥ 2). Denote $\parallel u\parallel_{1,\tau}=(\int_{\mathbb R^N}( \nab An Interpolation of … WebThe proof is based on the method of transplantation of Green's functions and without using the blow-up analysis method. As a consequence, we obtain a singular Moser--Trudinger … examples of a blackbody