共查询到20条相似文献,搜索用时 46 毫秒
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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. 相似文献
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给出了如下的非线性椭圆方程自由边值问题-Δu=λu+(1+ε)u+p,x∈B Rn,u|Ω=μ,∫Ωnu=-M(1)在C[0,1]中的球对称解的存在性.并得到比上述问题更一般的非线性椭圆方程自由边值问题-Δu=h(u),x∈B Rn,u|Ω=μ,∫Ωun=-M,在C[0,1]中的球对称解的存在性,其中B为Rn中的单位球,p>1,λ>0,μ<0,M>0,ε>0;λ,μ,M,ε均为常数,n为正整数. 相似文献
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应用Hodge分解定理,得到了非齐次A-调和方程-div(A(x,Du(x)))=f(x,u(x))对应的障碍问题很弱解的局部和全局的W~(1,q)(Ω)-正则性,其中,A(x,Du(x)),f(x,u(x))满足文中所给的条件,从而推广了相关文献中的有关结果.该结果在优化控制问题中有着广泛的应用. 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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鲍卫东 《数学的实践与认识》2006,36(6):229-235
讨论了半线性椭圆方程△u-a(x)u+6(x)up=0奇解的渐近性质,其中u Ω→R,Ω()Rn,n≥3, n/(n - 2) < p < (n + 2)/(n - 2). 相似文献
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本文讨论奇异扰动的拟线性椭圆型方程-ε△pu(x)=f(u(x)),u(x)≥0,x∈Ω;u=0,x∈Ω在Dirichlet边值条件下极小能量解的存在性和结构.其中ε>0是小参数,p>2,△pu=div(|Du|p-2Du),f(s)=sq-sp-1,p-1<q<Np/N-p-1.Ω RN(N≥2)是有界光滑区域.当ε→0时,方程存在一个极小能量解,应用移动平面方法可以证明此解在凸区域上会变成一个尖峰解. 相似文献
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《数学物理学报(A辑)》2017,(5)
该文研究了一类具退化强制项和自然增长条件梯度项的奇异椭圆方程的Dirichlet边值问题{-div((∣▽u∣~(p-2)▽u)/((1+∣u∣)~r)+B(∣▽u∣~p)/(∣u∣~θ)=f,x∈Ω,u0,x∈Ω,u=0,x∈аΩ,其中,ΩR~N(N≥p)是一有界区域,B,γ,θ0,P1,f是某一Lebesgue空间L~m(Ω)(m≥1)中的非负函数.利用截断技术并结合选取适当的检验函数,证明了该问题非负解的存在性以及正则性等结果.该文结果表明尽管低阶梯度项是奇异的,它的存在对解的正则性有"好"的影响. 相似文献
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Yu. N. Lin'kov 《Journal of Mathematical Sciences》1991,53(4):409-415
We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987. 相似文献
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A. P. Ushakova 《Journal of Mathematical Sciences》1998,89(5):1582-1589
An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some
conditions, the estimate has the order ε1/3L(ε), where L(ε) is a slowly varying function.
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I. 相似文献
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Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from... 相似文献
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本文研究了完全正则半群簇的子簇格[V+∩PV,V+∩PV]的某些格运算性质,我们证明了簇V+∩PV可分解为V与V+∩PV的并;对任意完全正则半群簇W,有W∩(V∨V+∩PV)=(W∩V)∨(W∩V+∩PV).特别地,我们得到了等式V+∩PV=V成立的若干条件. 相似文献
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S. V. Kerov 《Journal of Mathematical Sciences》1988,41(2):995-999
The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986. 相似文献
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A. N. Vetokhin 《Differential Equations》2016,52(3):272-281
We consider parametric families of differential systems with coefficients that are bounded and continuous on the half-line and uniformly in time continuously depend on a real parameter. For each Lyapunov exponent, we construct a family such that the Lyapunov exponent of its systems treated as a function of the parameter is not a lower semicontinuous function for any value of the parameter. 相似文献