修正的积分型求和算子在Orlicz空间中的逼近（英文）

本文介绍由Φ(x)构成的Orlicz空间L_Φ~*[0,∞),并介绍Orlicz空间的Hardy-Littlewood性质.然后给出Orlicz空间中修正的加权K-泛函与加权连续模的等价定理,最后建立修正的积分型求和算子在Orlicz空间中逼近的正、逆定理和等价定理.从而推广了该算在L_p[0,∞)空间中逼近性质.     

Sobolev方程的基于H~1-Galerkin混合方法的新分裂格式

正1引言考虑如下Sobolev方程u_t-▽·(a(x)▽u_t+a(x)▽u)+u=f(x,t),(x,t)∈Ω×J,u(x,t)=0,(x,t)∈аΩ×J,(1)u(x,0)=u_0(x),x∈Ω.其中Ω是R~d(d=1,2,3)中具有边界     

Bernstein-Durrmeyer算子拟中插式在Orlicz空间中的逼近

本文在Orlicz空间中研究了Bernstein-Durrmeyer算子拟中插式B_n~(2r-1)(f,x)逼近性质.利用2r阶Ditzian-Totik模与K-泛函的等价性,Jensen不等式,H?lder不等式,Berens-Lorentz引理得到了逼近的正,逆和等价定理,从而推广了Bernstein-Durrmeyer算子拟中插式B_n~(2r-1)(f,x)在L_P空间的逼近结果.     

二阶中立型泛函微分方程的周期解

考虑如下一类二阶中立型泛函微分方程的周期解:u″(t)-cu″(t-δ)+a(t)u(t)=λf(t,u(t-τ(t))),其中,λ>0为参数,c和δ为常数.通过应用Krasnoselskii锥不动点定理及一些分析技巧给出了这类方程周期正解的存在性非存在性和多解性.     

加权的Szász-Kantorovich-Bézier算子在Orlicz空间中的逼近等价定理（英文）

本文介绍了由Young函数生成的Orlicz空间L_Φ~*[0,∞),然后建立了修正的加权K-泛函与加权光滑模的等价定理,并利用它得到了加Jacobi权的Szász-Kantorovich-Bézier算子在Orlicz空间中逼近的正、逆和等价定理.     

具有凸凹项非齐次拟线性椭圆方程的多解性

在Orlicz—Sobolev空间中利用临界点理论考虑了非齐次拟线性椭圆方程{-div((︱▽u︱)▽u)=μ︱u︱q-2u+λ︱u︱p-2u在Ω中,u=0在Ω上无穷多解的存在性,其中Ω是R~N中边界光滑的有界区域,μ,λ∈R是两个参数.     

一类二阶拟线性椭圆型方程障碍问题的很弱解

本文在一定条件下,运用Hodge分解、Sobolev嵌入定理和Lp中的Minkcwski不等式等,研究二阶拟线性椭圆型方程divA(x,u,u)=0的障碍问题很弱解的性质.     

含有Sobolev-Hardy临界指标的奇异椭圆方程无穷多解的存在性

该文研究如下奇异椭圆方程-Δu- μu｜x｜2 =｜u｜2 (s) -2 u｜x｜s λ｜u｜q-2 u ,u∈H10 (Ω) ,　x∈Ω ,0 ≤ μ< μ =(N- 2 ) 24 ,其中Ω是RN 中的有界区域 ,0 ∈Ω ,N≥ 3.2 (s) =2 (N -s)N- 2 ( 0 ≤s≤ 2 )是临界Sobolev Hardy指标 ,1 相似文献   

含临界位势的广义平均曲率方程的解

讨论一个含临界位势的广义平均曲率方程在Dirichlet边界条件下解的存在性.此方程相应的变分泛函关于u的梯度非齐次,且Sobolev空间嵌入失去紧性.为了克服这些困难,本文将关于范数的一个基本结论推广到一般的偶泛函,并利用C.K.N不等式及Ambrosetti的山路引理证明了方程存在非平凡解.     

广义逆与Lax定理的推广

Lax定理是泛函分析中的一个重要结果。它在偏微分方程中有重要应用,它可表述如下: 若V是一个实的Hilbert空间,α(u,v)为V×V上的连续双线性泛函,且存在C>0使     

Symmetrization inequalities and Sobolev embeddings

We prove new extended forms of the Pólya-Szegö symmetrization principle. As a consequence new sharp embedding theorems for generalized Besov spaces are proved, including a sharpening of the limiting cases of the classical Sobolev embedding theorem. In particular, a surprising self-improving property of certain Sobolev embeddings is uncovered.

     

Strong convergence of the discontinuous Galerkin scheme for the low regularity miscible displacement equations

Strong convergence of the numerical solution to a weak solution is proved for a nonlinear coupled flow and transport problem arising in porous media. The method combines a mixed finite element method for the pressure and velocity with an interior penalty discontinuous Galerkin method in space for the concentration. Using functional tools specific to broken Sobolev spaces, the convergence of the broken gradient of the numerical concentration to the weak solution is obtained in the L² norm. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 489–513, 2017     

On the equivalence of fractional-order Sobolev semi-norms

We present various results on the equivalence and mapping properties under affine transformations of fractional-order Sobolev norms and semi-norms of orders between zero and one. Main results are mutual estimates of the three semi-norms of Sobolev–Slobodeckij, interpolation and quotient space types. In particular, we show that the former two are uniformly equivalent under affine mappings that ensure shape regularity of the domains under consideration.     

Sobolev-Type Classes of Functions with Values in a Metric Space. II

We prove equivalence of the definitions by the author and by Korevaar and Schoen of the Sobolev classes of mappings of a domain of an arithmetic n-dimensional space to a metric space.     

Harmonic vibration of prismatic shells in zero approximation of Vekua's hierarchical models

In this article elastic cusped symmetric prismatic shells (i.e., plates of variable thickness with cusped edges) in the zero approximation of I.Vekua's hierarchical models is considered. The well-posedness of the boundary value problems (BVPs) under the reasonable boundary conditions at the cusped edge and given displacements at the non-cusped edge is studied in the case of harmonic vibration. The approach works also for non-symmetric prismatic shells word for word. The classical and weak setting of the BVPs in the case of the zero approximation of hierarchical models is considered. Appropriate weighted functional spaces are introduced. Uniqueness and existence results for the variational problem are proved. The structure of the constructed weighted space is described and its connection with weighted Sobolev spaces is established. Moreover, some sufficient conditions for a linear functional arising in the right-hand side of the variational equation to be bounded are given.     

Higher-order symmetrization inequalities and applications

We prove new extended forms of the Pólya-Szegö symmetrization principle. As a consequence new sharp embedding theorems for generalized Sobolev and Besov spaces are proved.     

Variational approach to the solution of linear multiparameter eigenvalue problems

We associate a multiparameter spectral problem in a real Euclidean space with a variational problem of finding a minimum of a certain functional. We establish the equivalence of the spectralproblem and the variational problem. On the basis of the gradient procedure, we propose a numerical algorithm for the determination of its eigenvalues and eigenvectors. The local convergence of the algorithm is proved.     

Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains

The solvability in Sobolev spaces is proved for divergence form complex-valued higher order parabolic systems in the whole space, on a half-space, and on a Reifenberg flat domain. The leading coefficients are assumed to be merely measurable in one spacial direction and have small mean oscillations in the orthogonal directions on each small cylinder. The directions in which the coefficients are only measurable vary depending on each cylinder. The corresponding elliptic problem is also considered.     

On a parabolic logarithmic Sobolev inequality

In order to extend the blow-up criterion of solutions to the Euler equations, Kozono and Taniuchi [H. Kozono, Y. Taniuchi, Limiting case of the Sobolev inequality in BMO, with application to the Euler equations, Comm. Math. Phys. 214 (2000) 191-200] have proved a logarithmic Sobolev inequality by means of isotropic (elliptic) BMO norm. In this paper, we show a parabolic version of the Kozono-Taniuchi inequality by means of anisotropic (parabolic) BMO norm. More precisely we give an upper bound for the L^∞ norm of a function in terms of its parabolic BMO norm, up to a logarithmic correction involving its norm in some Sobolev space. As an application, we also explain how to apply this inequality in order to establish a long-time existence result for a class of nonlinear parabolic problems.     

On the Stokes system and on the biharmonic equation in the half‐space: an approach via weighted Sobolev spaces

In this paper, we investigate the Stokes system and the biharmonic equation in a half‐space of ?ⁿ. Our approach rests on the use of a family of weighted Sobolev spaces as a framework for describing the behaviour at infinity. A complete class of existence, uniqueness and regularity results for both the problems is proved. The proofs are mainly based on the principle of reflection. Copyright © 2002 John Wiley & Sons, Ltd.