Related papers: A Moser-Trudinger inequality for the singular Toda…
We establish the Trudinger-Moser inequality on weighted Sobolev spaces in the whole space, and for a class of quasilinear elliptic operators in radial form of the type $\displaystyle Lu:=-r^{-\theta}(r^{\alpha}\vert…
In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of R^n. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams' results to…
We establish Moser-Trudinger-Onofri inequalities under constraint of a deviation of the second order moments from $0$, which serves as an intermediate one between Chang-Hang's inequalities under first and second order moments constraints. A…
In this paper we obtain an inequality on the unit disc $B$ in the plane, which improves the classical Moser-Trudinger inequality and the classical Hardy inequality at the same time. Namely, there exists a constant $C_0>0$ such that \[…
The Trudinger-Moser inequality states that for functions $u \in H_0^{1,n}(\Omega)$ ($\Omega \subset \mathbb R^n$ a bounded domain) with $\int_\Omega |\nabla u|^ndx \le 1$ one has $\int_\Omega (e^{\alpha_n|u|^{\frac n{n-1}}}-1)dx \le c…
We solve a super Toda system on a closed Riemann surface of genus~$\gamma>1$ and with some particular spin structures. This generalizes the min-max methods and results for super Liouville equations and gives new existence results for super…
We prove that a certain sequence of tau functions of the Garnier system satisfies Toda equation. We construct a class of algebraic solutions of the system by the use of Toda equation; then show that the associated tau functions are…
A multi-linear variable separation approach is developed to solve a differential-difference Toda equation. The semi-discrete form of the continuous universal formula is found for a suitable potential of the differential-difference Toda…
We compute quantum corrections to soliton masses in affine Toda theories with imaginary exponentials based on the nonsimply-laced Lie algebras $c_n^{(1)}$. We find that the soliton mass ratios renormalize nontrivially, in the same manner as…
Calogero-Moser models and Toda models are well-known integrable multi-particle dynamical systems based on root systems associated with Lie algebras. The relation between these two types of integrable models is investigated at the levels of…
We consider the SU(3) Toda system on a compact surface. We give both existence and non-existence results under some conditions on the parameters. Existence results are obtained using variational methods, which involve a geometric inequality…
In this article, we firstly study the cone Moser-Trudinger inequalities and their best exponents $\alpha_2$ on both bounded and unbounded domains $\mathbb{R}^2_{+}$. Then, using the cone Moser-Trudinger inequalities, we study the existence…
We derive a sharp Moser-Trudinger inequality for the borderline Sobolev imbedding of W^{2,n/2}(B_n) into the exponential class, where B_n is the unit ball of R^n. The corresponding sharp results for the spaces W_0^{d,n/d}(\Omega) are well…
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…
In this paper, we use the method of blow-up analysis and capacity estimate to derive the singular Trudinger--Moser inequality involving $N$-Finsler--Laplacian and $L^{p}$ norm, precisely, for any $p>1$, $0\leq\gamma<\gamma_{1}:=…
This paper is devoted to the Moser-Trudinger-Onofri inequality on smooth compact connected Riemannian manifolds. We establish a rigidity result for the Euler-Lagrange equation and deduce an estimate of the optimal constant in the inequality…
Toda field theories are important integrable systems. They can be regarded as constrained WZNW models, and this viewpoint helps to give their explicit general solutions, especially when a Drinfeld-Sokolov gauge is used. The main objective…
Given $\alpha >0$, we establish the following two supercritical Moser-Trudinger inequalities \[ \sup\limits_{u \in W^{1,n}_{0,{\rm rad}}(B): \int_B |\nabla u|^n dx \leq 1} \int_B \exp\big( (\alpha_n + |x|^\alpha) |u|^{\frac{n}{n-1}} \big)…
We derive sharp Moser-Trudinger inequalities on the CR sphere. The first type is in the Adams form, for powers of the sublaplacian and for general spectrally defined operators on the space of CR-pluriharmonic functions. We will then obtain…
The classical inequality of Bohr concerning Taylor coeficients of bounded holomorphic functions on the unit disk, has proved to be of significance in answering in the negative the conjecture that if the non-unital von Neumann inequality…