Related papers: Extremal Functions for the Singular Moser-Trudinge…
Combining Carleson-Chang's result with blow-up analysis, we prove existence of extremal functions for certain Trudinger-Moser inequalities in dimension two. This kind of inequality was originally proposed by Adimurthi and O. Druet, extended…
Sharp Moser-Trudinger type inequalities and their extremal functions play an important role in studying nonlinear PDEs and geometry. We establish a new sharp Moser-Trudinger type inequality in the upper half space in two dimensions and…
In a previous paper, the author proved the existence of extremal function for the Moser-Trudinger inequality on a compact manifold. In the this paper, we will give a new proof of one of the key proposition.
In this paper, using blow-up analysis, we prove a singular Hardy-Morser-Trudinger inequality, and find its extremal functions. Our results extend those of Wang-Ye (Adv. Math. 2012), Yang-Zhu ( Ann. Glob. Anal. Geom. 2016), Csat\'{o}- Roy…
We study Moser-Trudinger type functionals in the presence of singular potentials. In particular we propose a proof of a singular Carleson-Chang type estimate by means of Onofri's inequality for the unit disk in $\mathbb{R}^2$. Moreover we…
In this paper, we investigate the extremal functions for anisotropic Trudinger-Moser inequalities. Our method uses convex symmetrization, the continuity of the supremum function, together with the relation between the supremums of the…
Our main purpose in this paper is to establish the existence and nonexistence of extremal functions for sharp inequality of Adimurthi-Druet type for fractional dimensions on the entire space. Precisely, we extend the sharp Trudinger-Moser…
In this paper we prove the existence of extremal functions for the Adams-Moser-Trudinger inequality on the Sobolev space $H^{m}(\Omega)$, where $\Omega$ is any bounded, smooth, open subset of $\mathbb{R}^{2m}$, $m\ge 1$. Moreover, we extend…
Given a compact closed four dimensional smooth Riemannian manifold, we prove existence of extremal functions for Moser-Trudinger type inequality. The method used is Blow-up analysis combined with capacity techniques.
In this paper the authors complete their study of the singular Moser-Trudinger embedding [G. Csato and P. Roy, Extremal functions for the singular Moser-Trudinger inequality in 2 dimensions, Calc. Var. Partial Differential Equations, DOI…
We prove the existence of extremals for fractional Moser-Trudinger inequalities in an interval and on the whole real line. In both cases we use blow-up analysis for the corresponding Euler-Lagrange equation, which requires new sharp…
We first prove a weighted inequality of Moser-Trudinger type depending on a parameter, in the two-dimensional Euclidean space. The inequality holds for radial functions if the parameter is larger than -1. Without symmetry assumption, it…
We establish critical and subcritical sharp Trudinger-Moser inequalities for fractional dimensions on the whole space. Moreover, we obtain asymptotic lower and upper bounds for the fractional subcritical Trudinger-Moser supremum from which…
We establish a supercritical Trudinger-Moser type inequality for the $k$-Hessian operator on the space of the $k$-admissible radially symmetric functions $\Phi^{k}_{0,\mathrm{rad}}(B)$, where $B$ is the unit ball in $\mathbb{R}^{N}$. We…
We extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincar\'e's inequality. We find out that the same equivalence does not hold in general for conformal metrics on the unit ball, showing counterexamples. We also…
On the space of weighted radial Sobolev space, the following generalization of Moser-Trudinger type inequality was established by Calanchi and Ruf in dimension 2 : If $\beta \in [0,1)$ and $w_0(x) = |\log |x||^\beta $ then $$ \sup_{\int_B…
The Adimurthi-Druet [1] inequality is an improvement of the standard Moser-Trudinger inequality by adding a $L^2$-type perturbation, quantified by $\alpha\in [0,\lambda\_1)$, where $\lambda\_1$ is the first Dirichlet eigenvalue of $\Delta$…
In a series of articles, Ryan Hynd and Francis Seuffert have studied extremal functions for the Morrey inequality. Building upon their work, we study the extremals of a Morrey-type inequality for fractional Sobolev spaces. We verify a few…
We establish a Trudinger-Moser type inequality with a Tintarev-type constraint in fractional-dimensional spaces and prove the existence of maximizers in the critical regime. Our results provide a refinement of those in (Calc. Var. 52…
The Moser-Trudinger embedding has been generalized in [Adimurthi A.; Sandeep K., A singular Moser-Trudinger embedding and its applications, \textit{NoDEA Nonlinear Differential Equations Appl.}, 13 (2007), no. 5-6, 585--603] to the…