由H\"{o}rmander向量场构成的抛物方程的 $W_{\ast}^{1,p}$ 正则性

设 $X_{1},\cdots ,X_{q}\ (q相似文献   

一类具间断系数退化椭圆型方程的$L^{p,\lambda}$正则性

得到一类退化椭圆型方程弱解梯度在其拟线性系数矩阵$A(\cdot,u)$对任意$u$关于$x$一致满足VMO条件下在Morrey空间$L^{p,\lambda}$的内部正则性.     

一类含测度的非强制拟线性椭圆方程解的存在性和不存在性

本文主要研究如下含非线性梯度项的非强制拟线性椭圆方程\begin{equation*}\left \{\begin{array}{rl}-\text{div}(\frac{|\nabla u|^{p-2}\nabla u}{(1+|u|)^{\theta(p-1)}})+\frac{|u|^{p-2}u|\nabla u|^{p}}{(1+|u|)^{\theta p}}=\mu,~&x\in\Omega,\\ u=0,~&x\in\partial\Omega,\end{array}\right.\end{equation*} 弱解的存在性和不存在性, 其中$\Omega\subseteq\mathbb{R}^N(N\geq3)$ 是有界光滑区域, $1相似文献   

$\mathbb{C}^{n}$中$\mu$-Bergman空间的刻画和微分复合算子

设$p>0$, $\mu$和$\mu_{1}$是$[0,1)$上的正规函数. 本文首先给出了$\mathbb{C}^{n}$中单位球上$\mu$-Bergman空间$A^{p}(\mu)$的几种等价刻画; 然后 分别刻画了$A^{p}(\mu)$到$A^{p}(\mu_{1})$的 微分复合算子$D_{\varphi}$为有界算子以及紧算子的充要条件, 同时给出了当$p>1$时$D_{\varphi}$为 $A^{p}(\mu)$到$A^{p}(\mu_{1})$上紧算子的一种简捷充分条件和必要条件.     

一类缺项算子矩阵的四类点谱的扰动

有界线性算子的点谱可进一步细分为4类,分别为$\sigma_{p1}$, $\sigma_{p2}$, $\sigma_{p3}$ 和$\sigma_{p4}$.设 $H, K$为无穷维可分的Hilbert空间,用$M_C$表示$2\times 2$上三角算子矩阵$\left(\begin{array}{cc} A & C \\ 0 & B \\ \end{array} \right)$,对于给定的 $A\in B(H),~B\in B(K)$,描述了集合$\bigcap\limits_{C\in B(K,H)}\sigma_{p1}(M_C)$, $\bigcap\limits_{C\in B(K,H)}\sigma_{p2}(M_C)$, $\bigcap\limits_{C\in B(K,H)}\sigma_{p3}(M_C)$和$\bigcap\limits_{C\in B(K,H)}\sigma_{p4}(M_C)$.     

非齐性广义Morrey空间上双线性强奇异Calder\''{o}n-Zygmund算子及交换子

本文的主要建立非齐性度量测度空间上双线性强奇异积分算子$\widetilde{T}$及交换子$\widetilde{T}_{b_{1},b_{2}}$在广义Morrey空间$M^{u}_{p}(\mu)$上的有界性. 在假设Lebesgue可测函数$u, u_{1}, u_{2}\in\mathbb{W}_{\tau}$, $u_{1}u_{2}=u$,且$\tau\in(0,2)$. 证明了算子$\widetilde{T}$是从乘积空间$M^{u_{1}}_{p_{1}}(\mu)\times M^{u_{2}}_{p_{2}}(\mu)$到空间$M^{u}_{p}(\mu)$有界的, 也是从乘积空间$M^{u_{1}}_{p_{1}}(\mu)\times M^{u_{2}}_{p_{2}}(\mu)$到广义弱Morrey空间$WM^{u}_{p}(\mu)$有界的,其中$\frac{1}{p}=\frac{1}{p_{1}}+\frac{1}{p_{2}}$及$1相似文献   

强奇异Calder-Zygmund积分及其交换子在 Hardy 型空间上的有界性

给出了局部 Hardy 空间 $h^{p}(\mathbb{R}^{n})$\ $\big(\frac{n}{n+1}相似文献   

Zygmund微分映射的正则点

该文的主要结果是: 对任意Zygmund类$C^{p,Z}$映射$f:R^{n}\rightarrow R^{m}$, 若$\frac{n-m}{2}\leq p\leq n-m-1$, 则有mes$K_{f}>0$或者mes$C_{f}>0$. 这个结果给出了Hirsch问题的部分回答.     

$L^{p}_{[0,1]}$空间M\"{u}ntz有理逼近的Jackson型估计 (英)

设$\Lambda=\{\lambda_{n}\}_{n=1}^{\infty}$为正的实数数列, 且当$n\rightarrow\infty$时, 有$\lambda_{n}\searrow 0$.本文给出了当 $\lambda_{n}\leq Mn^{-\frac{1}{2}},\;n=1,2, \cdots ,$(其中$M>0$为一正常数)时M\"{u}ntz系统$\{x^{\lambda_n}\}$的有理函数在$ L_{[0,1]} ^{p}$空间的逼近速度,主要结论为$R_{n} (f, \Lambda )_{L^{p}}\leq C_M \omega (f, n^{-\frac{1}{2}})_{L^{p}},\;1 \leq p \leq \infty.$     

一类深度1的可迁模Lie超代数

建立了满足如下条件的可迁$\mathbb{Z}$-分次模Lie超代数$\frak{g}=\oplus_{-1\leq i\leq r}\frak{g}_{i}$的嵌入定理:(i) $\frak{g}_{0}\simeq \widetilde{\mathrm{p}}(\frak{g}_{-1}) $ 并且$\frak{g}_{0}$-模 $\frak{g}_{-1}$ 同构于$\widetilde{\mathrm{p}}(\frak{g}_{-1})$的自然模;(ii) $\dim \frak{g}_1=\frac 23 n(2n^2+1),$ 其中 $n=\frac{1}{2} \dim \frak{g}_{-1}.$特别地, 证明了满足上述条件的有限维单模Lie超代数同构于奇Hamilton模Lie超代数.对局限Lie超代数也做了相应的讨论.     

HEAT FLOW FOR YANG-MILLS-HIGGS FIELDS, PART I HEAT FLOW FOR YANG-MILLS-HIGGS FIELDS, PART I

1. IntroductionLet (M, g) be a four dimensional Riemannian manifold and let P be a principal bundlewith compact Lie structure group G over M. The Yang-Mills functional is defined bywhere F denotes the curvature of a connection D and dM is the volume form induced bythe metric g on M. All integrals on M in this paper will be with the volume form dM, sowe will not write it explicitly.Donaldsonl3] and K. Uhlenbeck[18'19] obtained many important results about Yang-Millsequations (see also […     

HEAT FLOW FOR YANG-MILLS-HIGGS FIELDS, PART I

The Yang-Mills-Higgs field generalizes the Yang-Mills field. The authors establish the local existence and uniqueness of the weak solution to the heat flow for the Yang-Mills-Higgs field in a vector bundle over a compact Riemannian 4-manifold, and show that the weak solution is gauge-equivalent to a smooth solution and there are at most finite singularities at the maximum existing time.     

THE LOCAL AND GLOBAL EXISTENCE OF THE SOLUTIONS OF HYPERBOLIC-PARABOLIC SYSTEM MODELING BIOLOGICAL PHENOMENA

The authors prove the local existence and uniqueness of weak solution of a hyperbolic-parabolic system and establish the global existence of the weak solution for this system for the spatial dimension n = 1.     

The Existence and Long-Time Behavior of Weak Solution to Bipolar Quantum Drift-Diffusion Model

The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.     

SEMICLASSICAL LIMIT FOR BIPOLAR QUANTUM DRIFT-DIFFUSION MODEL

Semiclassical limit to the solution of transient bipolar quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical bipolar drift-diffusion model. In addition, the authors also prove the existence of weak solution.     

On the finite element approximation of incompressible flows of an electrically conducting fluid

We consider the finite element approximation of incompressible flows field of an electrically conducing fluid in the presence of a magnetic where it is assumed that this field is prescribed. A weak form is chosen that is similar in some respects to a weak form used by many authors for the Navier-Stokes equations. Existence and uniqueness results are presented for the weak problem. A finite element Algorithm is given for the approximate solution of the weak problem and error estimates are derived.     

R~2上一类非牛顿流体动力学方程组解的最优衰减率

本文利用Fourier分解方法讨论一类二维不可压缩非牛顿流体动力学方程组弱解的衰减性,证明了弱解在L~2范数下衰减率为(1+t)~(-1/2),和线性热传导方程解的衰减率一致,在此意义下本文的结果是最优的。     

Trajectory Attractors for Binary Fluid Mixtures in 3D

Two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered.They consist of the 3D incompressible Navier-Stokes equations,subject to time-dependent external forces and coupled with either a convective Allen-Cahn or Cahn-Hilliard equation.Such systems can be viewed as generalizations of the Navier-Stokes equations to two-phase fluids.Using the trajectory approach,the authors prove the existence of the trajectory attractor for both systems.     

一类非线性发展方程弱解的长时间性态

本文分别在全空间和半空间两种情形下讨论一类非线性发展方程弱解的长时间性态．证明了其弱解在L^2范数下衰减速率和线性热方程一致，分别为t^-n/2(1-r-1/2)和t^-n/2(1/r-1/2)-1/2。     

ON THE EXISTENCE OF ALMOST GLOBAL WEAK SOLUTION TO MULTIDIMENSIONAL VLASOV-POISSON EQUATION

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