Related papers: Trudinger-Moser inequalities on complete noncompac…

In [16], we established Trudinger-Moser inequalities for complete noncompact Riemannian manifold on which the Ricci curvature has lower bound and the injectivity radius is strictly positive. In this note, we improve those inequalties when…

In the first part of the paper we investigate some geometric features of Moser-Trudinger inequalities on complete non-compact Riemannian manifolds. By exploring rearrangement arguments, isoperimetric estimates, and gluing local uniform…

Trudinger-Moser inequality is a substitute to the (forbidden) critical Sobolev embedding, namely the case where the scaling corresponds to $L^\infty$. It is well known that the original form of the inequality with the sharp exponent (proved…

In this paper a quasi-linear elliptic equation in the whole Euclidean space is considered. The nonlinearity of the equation is assumed to have exponential growth or have critical growth in view of Trudinger-Moser type inequality. Under some…

In this note, we give a new proof of subcritical Trudinger-Moser inequality on $\mathbb{R}^n$. All the existing proofs on this inequality are based on the rearrangement argument with respect to functions in the Sobolev space…

We give a new proof of the almost sharp Moser-Trudinger inequality on compact Riemannian manifolds based on the sharp Moser inequality on Euclidean spaces. In particular we can lower the smoothness requirement of the metric and apply the…

We introduce the concept of Calder\'on-Zygmund inequalities on Riemannian manifolds. For $1<p<\infty$, these are inequalities of the form $$ \left\Vert \mathrm{Hess}\left( u\right) \right\Vert _{L^p}\leq C_{1}\left\Vert u\right\Vert…

Let $M$ be a complete, simply connected Riemannian manifold with negative curvature. We obtain some Moser-Trudinger inequalities with sharp constants on $M$.

Continuing our previous work (Cohn, Lam, Lu, Yang, Nonlinear Analysis (2011), doi: 10.1016 /j.na.2011.09.053), we obtain a class of Trudinger-Moser inequalities on the entire Heisenberg group, which indicate what the best constants are. All…

We prove estimates and existence results for some fully nonlinear elliptic equations on Riemannian manifolds. These equations are not arbitrary, but arise naturally in the study of conformal geometry.

Motivated by a recent work of X. Chen and M. Zhu (Commun. Math. Stat., 1 (2013) 369-385), we establish a Trudinger-Moser inequality on compact Riemannian surface without boundary. The proof is based on blow-up analysis together with…

We study existence of maximizer for the Trudinger-Moser inequality with general nonlinearity of the critical growth on $R^2$, as well as on the disk. We derive a very sharp threshold nonlinearity between the existence and the non-existence…

This paper is to study the conformal scalar curvature equation on complete noncompact Riemannian manifold of nonpositive curvature. We derive some estimates and properties of supersolutions of the scalar curvature equation, and obtain some…

We are concerned with nonexistence results of nonnegative weak solutions for a class of quasilinear parabolic problems with a potential on complete noncompact Riemannian manifolds. In particular, we highlight the interplay between the…

In this paper, we establish a weighted Trudinger-Moser type inequality with the full Sobolev norm constraint on the whole Euclidean space. Main tool is the singular Trudinger-Moser inequality on the whole space recently established by…

We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian…

We obtain sharp estimates for heat kernels and Green's functions on complete noncompact Riemannian manifolds with Euclidean volume growth and nonnegative Ricci curvature. We will then apply these estimates to obtain sharp Moser-Trudinger…

In this paper we obtain Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities with sharp constants on Riemannian manifolds with non-positive sectional curvature and, in particular, a variety of new estimates on…

We establish Sobolev and Moser-Trudinger inequalities with best constants on noncompact Riemannan manifolds with Ricci curvature bounded below, and positive injectivity radius.

The main purpose of this short note, on the one hand, to is rigorize some part of the proof of Theorem 1.3 in [11] in a simple way, and on the other hand, to give an alternative argument from local inequalities to global ones.