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很弱解
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  very weak solution
     In this paper, we study the property of the very weak solution to obstacle problems for elliptic equationdivA(x,▽u(x)):O,which satisfies the conditions A(x,ξ)·ξ≥α|ξ|P,|A(x,ξ)|≤β(|ξ|+k(x))p-1,here 1
     研究二阶拟线性散度型椭圆方程divA(x,▽u(x))=0的障碍问题的很弱解的性质,此A-调和方程需满足A(x,ξ)·ξ≥α|ξ|p,|A(x,ξ)|≤β(|ξ|+k(x))p-1,其中1
短句来源
     Then we establish the regularity of very weak solutions of Beltrami system:there exist integrable exponents r 1 and r 2 (1very weak solution f∈W 1,r 1 loc (Ω,R n)of Beltrami system belongs to W 1,r 2 loc (Ω,R n). So f is still a classical weak solution of Beltrami system.
     从而来建立Beltrami方程组很弱解的正则性:存在可积指数r1和r2,1<r1<n<r2<∞,使得方程组在低于自然可积指数Sobolev空间W1,r1loc(Ω,Rn)中的很弱解,都属于空间W1,r2loc(Ω,Rn),即:f仍是经典意义下的弱解
短句来源
     We show this: let \$f\$ belong to \$\+\{1,n-2\}(Ω)\$, which is a subspace of Morrey space \$L\+\{1,n-2\}(Ω)\$, the very weak solution of the equation is in VMO space locally.
     本文表明 :若f属于Morrey空间L1 ,n- 2 (Ω)的某个子空间 L1 ,n - 2 (Ω) ,则对应的很弱解属于局部的VMO空间 .
短句来源
     This paper studies the property of the very weak solution to obstacle problems for weighted elliptic equation-div A(x,u(x))=0.
     研究加权形式的二阶拟线性散度型椭圆方程-divA(x,u(x))=0的障碍问题的很弱解的性质。
短句来源
     Using Hodge decomposition theorem, this paper discuss the f usion problem of very weak solution on nonhomogeneous A-harmonic equations-divA(x,u)=B(x,u,u).
     本文使用Hodge分解理论 ,讨论了一类非齐次A 调和方程 -divA(x , u) =B(x ,u ,Du)很弱解的合并问题 .
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  very weak solutions
     Using Hodge decomposition theorem, this paper obtains W1,q -regularity for very weak solutions to non-homogeneous A-harmonic systems-Di(Aij(x,u,Du))+Bj(x,u,Du) = 0, j = 1,… ,m and generalizes the corresponding results in [6-8].
     本文应用Hodge分解定理,得到了非齐次A-调和方程组 -Di(Aij(x,u,Du))+Bj(x,u,Du)=0,j=1,…,m的很弱解的局部W1,q-正则性,从而推广了文献[6-8]有关的结果.
短句来源
     Then we establish the regularity of very weak solutions of Beltrami system:there exist integrable exponents r 1 and r 2 (1
     从而来建立Beltrami方程组很弱解的正则性:存在可积指数r1和r2,1<r1<n<r2<∞,使得方程组在低于自然可积指数Sobolev空间W1,r1loc(Ω,Rn)中的很弱解,都属于空间W1,r2loc(Ω,Rn),即:f仍是经典意义下的弱解
短句来源
     Using a pointwise inequality for Sobolev functions in terms of maximum function to construct a global Lipschitz continuous test function,the authors obtain uniqueness re- sults for very weak solutions in grand Sobolev space W_0~(θ,p)) (Ω) to non-linear elliptic equation -divA(x,u,Du)=f(x) satisfying certain conditions.
     利用以极大函数表示的有关Sobolev函数的逐点不等式来构造全局的Lipschitz型检验函数,得到了,在一定条件下,拟线性椭圆方程-div A(x,u,Du)=f(x)在grand Sobolev空间W_0~(θ,p)(Ω)中的很弱解是唯一的.
短句来源
     The regularity result is proved by using the technique of Hodge decomposition and reverse Hlder inequality. There exists: q1, p′(q1=q1very weak solutions of A-harmonic equations u∈W1,q1loc(Ω,Rn) , we have u∈W1,q′loc(Ω,Rn) .
     利用Hodge分解、逆Hlder不等式等工具证明了其正则性结果存在两个可积指数q1=q1(n,l,k1,k2)很弱解u∈W1lo,cq1(Ω,Rn),都有u∈Wl1o,cp'(Ω,Rn)
短句来源
     Zeros for the Gradients of Very Weak Solutions of a Class of Elliptic Equation of Divergence Type
     一类散度型椭圆方程很弱解梯度的零点
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  “很弱解”译为未确定词的双语例句
     A regularity result of a class of second order divergence form elliptic equation was obtained .
     得到了一类二阶散度型椭圆方程很弱解的一个正则性结果。
短句来源
     On Very Weak Solutions of Beltrami System
     关于 Beltrami 方程组的很弱解
短句来源
     Many interesting results have been obtained for the solutions of harmonic equation and their obstacle problems, however the definition and regularity results for nonhomogeneous elliptic equation (1.1) stall be unknown.
     近年来对调和方程及其障碍问题解的正则性研究有了很大进展,但关于非齐次椭圆形方程(1.1)的障碍问题很弱解的定义和正则性结论仍未有结果。
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  very weak solution
We prove the existence of the very weak solution of the Dirichlet problem for the Navier-Stokes system with L2 boundary data.
      
  very weak solutions
Regularity for very weak solutions to A-harmonic equation
      
We develop a theory for a general class of very weak solutions to stationary Stokes and Navier-Stokes equations in a bounded domain Ω with boundary ?Ω of class C2,1, corresponding to boundary data in the distribution space W-1/q,q(?Ω), 1>amp;lt;q>amp;lt;∞.
      
We investigate a class of weak solutions, the so-called very weak solutions, to stationary and nonstationary Navier-Stokes equations in a bounded domain
      
Very weak solutions of parabolic systems ofp-Laplacian type
      
We examine the possibility of using NMR and other measurements on very weak solutions of3He in liquid4He to investigate the superfluid phase transition.
      
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By considering each component of vector functions,we transform Beltrami system to a class of elliptic systems of divergence type.Then we establish the regularity of very weak solutions of Beltrami system:there exist integrable exponents r 1 and r 2 (1

从考虑向量值函数的每一个分量出发,将Beltrami方程组转化为一类散度型椭圆组;从而来建立Beltrami方程组很弱解的正则性:存在可积指数r1和r2,1<r1<n<r2<∞,使得方程组在低于自然可积指数Sobolev空间W1,r1loc(Ω,Rn)中的很弱解,都属于空间W1,r2loc(Ω,Rn),即:f仍是经典意义下的弱解

In this paper, we improve the integrability of the derivatives of very weak solutions for a class of nonlinear elliptic systems (1.1). which satisfy. the controllable growth conditions (1.2)-(1.4).

本文在可控增长条件(1.2)-(14)下,对一类非线性椭圆方程组(1.1)改进其很弱解偏微商的可积性,使其为经典意义下的弱解.

The uniqueness result of very weak solutions of beltrami system is obtained by using Hodge decomposition.

本文利用 Hodge分解 ,给出了 Beltrami方程组很弱解的唯一性结果

 
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