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

A quasi-linear elliptic equation with critical growth on compact Riemannian manifold without boundary

“…The proof of Theorem 1.1 is based on (1.2) and the Young inequality in a nontrivial way. Similar idea has been used by Adimurthi and the second named author [3]. A special case of Theorem 1.1 is m = 1, which is also known by Li 2 6) where u S 1,τ is defined by (1.4) Next we study the existence of solutions to the following quasi-linear equation:…”

Extremal Functions for Trudinger-Moser Type Inequalities in ℝ^N

“…Later, using the Young inequality, Adimurthi-Yang [12] provided a very simple proof of the critical Trudinger-Moser inequality in R N , as well as the singular Trudinger-Moser inequality.…”

Existence of Nontrivial Weak Solutions to Quasi-linear Elliptic Equations with Exponential Growth

“…2) is closely related to a singular Trudinger-Moser type inequality [15]. That is, for all α > 0, 0 β < n, and u ∈ W 1,n (R n ) (n 2), there holds…”

“…Panda [11], doÓ et al [12,13] and Alevs-Figueiredo [14] studied problem (1.2) in general dimension and β = 0. When β = 0, (1.2) was studied by Adimurthi-Yang [15], doÓ et al [16], Yang [17], Zhao [18], and others. Similar problems in R 4 or complete noncompact Riemannian manifolds were also studied by Yang [19,20].…”