共查询到16条相似文献,搜索用时 46 毫秒
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该文引入一类新的函数空间, 并借助于此空间, 研究了 A -调和方程很弱解的弱单调性, 并得到了空间Beltrami方程组弱解分量函数的弱单调性. 相似文献
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偶数维空间上广义Beltrami方程组及高维空间的Beltrami方程组 总被引:3,自引:0,他引:3
本文在n=2l维偶数空间上得到广义Beltrami方程组Dtf(x)H(x)Df(x)=J(x,f)2/nG(x)的伸张公式,并在H(x)为对角阵的条件下,给出广义Beltrami方程组的正则性定理,Caciopoli型不等式和可去性定理.此外,还将所有维数的Beltrami方程组Dtf(x)Df(x)=J(x,f)2/nG(x)化为一个“Beltrami方程” 相似文献
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双特征的Beltrami方程和拟正则映射 总被引:9,自引:2,他引:7
设Ω为Rn上的一个区域,n2,对于具有双特征矩阵G(x),H(x)∈Ck,α(Ω,Rn),k1,0<α<1的Beltrami方程(1.4),建立了在Sobolev空间W1,nloc(Ω,Rn)上广义解的正则性:f(x)∈Ck+1,δloc(Ω),对某一δ:0<δ<1. 相似文献
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使用Hodge分解得到了下列结果 :若f∈W1,n(1-ε)0 (Ω ,Rn) ,n>33为Beltrami方程组 (1 )的广义解 ,并且ε<14× 1 0 4lognabn/2 ,这里a与b来自 (2 ) ,则f=0 ,a .e.Ω . 相似文献
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该文研究空间Beltrami方程的推广形式,即双特征Beltrami方程.利用外微分形式与矩阵的外代数等工具,将双特征Beltrami方程转化为一个非齐次的狆 调和方程,转化过程中只用到加于特征矩阵的一致椭圆型条件.然后验证了算子犃满足的条件:Lipschitz型条件、单调不等式、齐次性条件以及算子犅满足的控制增长条件.并利用得到的狆 调和方程,给出了双特征Beltrami方程广义解分量函数的弱单调性结果. 相似文献
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一类散度型椭圆方程的很弱解 总被引:2,自引:1,他引:1
本文研究满足一致椭圆型条件的散度型椭圆方程 ∑ni,j=1ddxjai,j(x) dudxi =0的很弱解 ,并以Hodge分解和弱逆H lder不等式为工具 ,证明了其正则性结果 :对任意的 2 - 2 n 1× 1 0 0 n2βα( 2 n 2 1 ) 2 -12 ,使得对其任意很弱解u∈W1r,loc(Ω) ,都有u∈W1p ,loc(Ω) .特别 ,u是其通常意义下的弱解 . 相似文献
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A-调和方程弱解的双权Caccioppoli型不等式 总被引:3,自引:1,他引:2
研究形如div A(x,u(x))=0的A-调和方程,证明了其弱解满足局部Aλr双权Caccioppoli型不等式.其中算子A:Ω×Rn→Rn满足如下条件:对于正常数0相似文献
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Regularity Results for the
Generalized Beltrami System 总被引:1,自引:0,他引:1
Abstract
For the generalized Beltrami system with two
characteristic matrices, we deal with the regularity of its very
weak solutions in the Sobolev class
(1 <
r <
n). By changing the
generalized Beltrami system into a class of a divergent elliptic
system with nonhomogeneous items, we obtain that each of its
very weak solutions is essentially a classical weak solution of
a usual Sobolev class. Furthermore, we also establish a higher
regularity of its weak solution if the regularity hypotheses of
two characteristic matrices are improved.
Supported by the National Natural Science Foundation
of China (49805005) and by the research foundation of Northern
Jiaotong University (2002SM061) 相似文献
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We study a new Liouville-type phenomenon for entire weak supersolutions of elliptic partial differential equations of the form A(u)=0 on , n2. Typical examples of the operator A(u) are the p-Laplacian for p>1, the mean curvature operator, and their well-known modifications. 相似文献
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Roman Shvydkoy 《Journal of Mathematical Analysis and Applications》2009,349(2):583-595
It is known that the energy of a weak solution to the Euler equation is conserved if it is slightly more regular than the Besov space . When the singular set of the solution is (or belongs to) a smooth manifold, we derive various Lp-space regularity criteria dimensionally equivalent to the critical one. In particular, if the singular set is a hypersurface the energy of u is conserved provided the one-sided non-tangential limits to the surface exist and the non-tangential maximal function is L3 integrable, while the maximal function of the pressure is L3/2 integrable. The results directly apply to prove energy conservation of the classical vortex sheets in both 2D and 3D at least in those cases where the energy is finite. 相似文献
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