Refinement of Hardy's inequalities via superquadratic and subquadratic functions

A new refined weighted Hardy inequality for p?2 is proved and discussed. The inequality is reversed for 1<p?2, which means that for p=2 we have equality. The main tool in the proofs are some new results for superquadratic and subquadratic functions.     

Regularity for weakly Dirac-harmonic maps to hypersurfaces

We prove that a weakly Dirac-harmonic map from a Riemann spin surface to a compact hypersurface is smooth. Supported by IMPRS “Mathematics in the Sciences” and the Klaus Tschira Foundation.     

Quasilinear elliptic equations with subquadratic growth

In this paper we consider nonlinear boundary value problems whose simplest model is the following:

(0.1)     

Multiple solutions for a Neumann system involving subquadratic nonlinearities

In this paper, we consider the model semilinear Neumann system

(N_λ)     

Homoclinic solutions for a class of subquadratic second-order Hamiltonian systems

In this paper, we study the existence of infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems. By using the variant fountain theorem, we obtain a new criterion for guaranteeing that second-order Hamiltonian systems has infinitely many homoclinic solutions. Recent results from the literature are generalized and significantly improved. An example is also given in this paper to illustrate our main results.     

Popoviciu's inequality for functions of several variables

T. Popoviciu (1965) [13] has proved an interesting characterization of the convex functions of one real variable, based on an inequality relating the values at any three points x₁,x₂,x₃, with the values at their means of different orders: (x₁+x₂)/2, (x₂+x₃)/2, (x₃+x₁)/2 and (x₁+x₂+x₃)/3. The aim of our paper is to develop a higher dimensional analogue of the usual convexity based on his characterization.     

Partial Hölder continuity for solutions of subquadratic elliptic systems in low dimensions

We consider weak solutions of second order nonlinear elliptic systems in divergence form under standard subquadratic growth conditions with boundary data of class C¹. In dimensions n∈{2,3} we prove that u is locally Hölder continuous for every exponent outside a singular set of Hausdorff dimension less than n−p. This result holds up to the boundary both for non-degenerate and degenerate systems. In the proof we apply the direct method and classical Morrey-type estimates introduced by Campanato.     

Existence of a periodic solution for subquadratic second-order discrete Hamiltonian system

Some solvability conditions of periodic solutions are obtained for a class of nonautonomous subquadratic second-order discrete Hamiltonian system by minimax methods in critical point theory.     

Remarks on multiplicity of solutions for a subquadratic elliptic equation

We consider a subquadratic elliptic equation in a bounded domain Ω⊂R^N$\Omega \subset {\mathbb{R}}^N$ (N?1$N?1$). By the Clark Theorem, we obtain the existence and multiplicity of its nontrivial solutions, and we show that this result has a great relationship with Ω itself. The above argument can be extended to biharmonic equations.     

波网络系统的适定性和正则性

研究了一波网络系统,在此网络的两个外部节点处施加控制并放置同位观测器,通过选择合适状态空间,将系统方程转化为抽象线性系统的形式.利用能量乘子法验证观测算子是允许的,通过对偶性原理得到控制算子也是允许的.求出传递函数后并验证传递函数在某个右半平面一致有界,从而说明系统是适定的,再求出传递函数在实轴上正方向的无穷远处的极限,找到直接传输算子,进而说明系统的正则性.     

Regularity properties of nonlocal minimal surfaces via limiting arguments

We prove an improvement of flatness result for nonlocal minimal surfaces which is independent of the fractional parameter s   when s→1⁻$s\to 1^{-}$.     

Regularity of refinable functions with exponentially decaying masks

The regularity of refinable functions is an important issue in all multiresolution analysis and has a strong impact on applications of wavelets to image processing, geometric and numerical solutions of elliptic partial differential equations. The purpose of this paper is to characterize the regularity of refinable functions with exponentially decaying masks and a dilation matrix whose eigenvalues have the same modulus. The main results of this paper are really extensions of some results in Cohen et al. (1999) [5], Jia (1999) [17] and Lorentz and Oswald (2000) [28].     

Periodic and subharmonic solutions of a class of subquadratic second-order Hamiltonian systems

Some solvability conditions of periodic and subharmonic solutions are obtained for a class of subquadratic nonautonomous second-order Hamiltonian systems by the minimax methods in critical point theory.     

Some starlikeness criterions for analytic functions

We determine a condition on M, α, λ and μ for which

     

Rank functions of strict cg-matroids

A matroid-like structure defined on a convex geometry, called a cg-matroid, is defined by Fujishige et al. [Matroids on convex geometries (cg-matroids), Discrete Math. 307 (2007) 1936-1950]. A cg-matroid whose rank function is naturally defined is called a strict cg-matroid. In this paper, we give characterizations of strict cg-matroids by their rank functions.     

Duality between quasi-concave functions and monotone linkage functions

A function F defined on the family of all subsets of a finite ground set E is quasi-concave, if F(X∪Y)≥min{F(X),F(Y)} for all X,Y⊆E. Quasi-concave functions arise in many fields of mathematics and computer science such as social choice, graph theory, data mining, clustering and other fields. The maximization of a quasi-concave function takes, in general, exponential time. However, if a quasi-concave function is defined by an associated monotone linkage function, then it can be optimized by a greedy type algorithm in polynomial time. Recently, quasi-concave functions defined as minimum values of monotone linkage functions were considered on antimatroids, where the correspondence between quasi-concave and bottleneck functions was shown Kempner and Levit (2003) [6]. The goal of this paper is to analyze quasi-concave functions on different families of sets and to investigate their relationships with monotone linkage functions.     

Stability of a functional equation deriving from cubic and quadratic functions

In this paper we establish the general solution of the functional equation 6f(x+y)−6f(x−y)+4f(3y)=3f(x+2y)−3f(x−2y)+9f(2y) and investigate the Hyers-Ulam-Rassias stability of this equation.     

Plateaudness of Kasami APN functions

It is shown that the Kasami function defined on ${\mathbb{F}}_{2^n}$ with n even is plateaued. This generalizes a result [3, Theorem 11], where the restriction $(n,3)=1$ is assumed. The result is used to establish the CCZ-inequivalence of the Kasami function defined on ${\mathbb{F}}_{2^n}$ with n even to the other known monomial APN functions [4].     

磁流体力学方程(MHD)几个新的正则性条件

该文考虑3维的磁流体力学方程,得到了方程的Leray-Hopf解的一些新的正则性条件.