-方程在逐片C~2-边界开集上的积分算子解

运用最近由Ｂｏｎｎｅａｎ和Ｄｉｅｄｅｒｉｃｈ〔１〕得到的方法，将－方程的解算子的局部积分构造方法进行了拓广和改进，并使其应用到具逐片Ｃ２－边界的开集上，给出了－方程的积分算子解中的不全纯依赖于Ｌｅｒａｙ映射的积分算子解     

On Liouville type theorems for fully nonlinear elliptic equations with gradient term

In this paper, we prove a Hadamard property and Liouville type theorems for viscosity solutions of fully nonlinear elliptic partial differential equations with a gradient term, both in the whole space and in an exterior domain.     

关于极大算子的线性化

V,M为函数空间,M■Lp(Rd).对ε∈Λ,Tε:V→M为一个线性算子.N:Rd→Λ为有限值函数.说明了当Λ=N或诸Tε都下半连续时,诸TN的一致弱(或强)有界性蕴含极大算子的相应有界性.     

Deriving Energy-Gap of Some Hamiltonians with Kinetic Coupling by the Invariant Eigen-Operator Method

We begin with proposing a unitary operator responsible for diagonalizing the Hamiltonian with kinetic couplings in particle physics to get a new form of Hamiltonian which has no coupling terms. By virtue of the invariant eigen-operator (IEO) method we search for the invariant eigen-operators for the new Hamiltonian. In this way the energy-gap of the Hamiltonians can be naturally obtained. This method may be generalized to N-mode Hamiltonian with kinetic couplings case. Work supported by the National Natural Science Foundation of China under grant 10475056 and Foundation of President of Chinese Academy of Science.     

Statistical stationary states for a two-layer quasi-geostrophic system

Existence of a family of locally invariant probability measures for large scale flows in enclosed temperate sea is proved. This model is extremely important for understanding the meso-scale phenomena in oceans. The techniques used are those developed by Albeverio and his collaborators.     

用弱孤立算子或弱外孤立算子确定闭包系统

引入了弱孤立算子和弱外孤立算子的概念,证明了对每个给定的集合X,可以给WI(X)(X上弱孤立算子的全体)和WOI(X)(X上的弱外孤立算子的全体)上赋予适当的序关系≤,使得(WI(X),≤)和(WOI(X),≤)是与(CS(X),)同构的完备格,这里CS(X)是X上的闭包系统的全体.因此可以用弱孤立算子或弱外孤立算子确定闭包系统.     

关于带m-增生算子扰动的非线性方程具误差的强收敛迭代序列

研究了在任意Banach空间,形如f∈Tx+Ax+Cx的非线性方程的解的逼近问题.其中T:E→2E为m-增生的,A:E→E是增生的,C:E→E是一个满足适当条件的非线性映射.构造了一个新的迭代序列,求得这一迭代序列的极限即为该方程的逼近解,从而推广了有关文献中的某些结果.