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1.
In this paper, we obtain two results of weak solutions to variational inequalities of triangular form under controllable growth and a class of natural growth conditions, i.e. 1^°. L^p-estimate for the gradient; 2^°. C^{1,β}_{loc}(Ω, R^N) regularity. 相似文献
2.
J. Y. Bello Cruz R. Díaz Millán 《Journal of Optimization Theory and Applications》2014,161(3):728-737
We propose a direct splitting method for solving a nonsmooth variational inequality in Hilbert spaces. The weak convergence is established when the operator is the sum of two point-to-set and monotone operators. The proposed method is a natural extension of the incremental subgradient method for nondifferentiable optimization, which strongly explores the structure of the operator using projected subgradient-like techniques. The advantage of our method is that any nontrivial subproblem must be solved, like the evaluation of the resolvent operator. The necessity to compute proximal iterations is the main difficulty of other schemes for solving this kind of problem. 相似文献
3.
The paper mainly concerns the study of a parametric weak vector variational inequality. Robinson’s metric regularity and Lipschitzian
stability of the solution mapping for the parametric weak vector variational inequality are firstly established. Then sensitivity
analysis of the solution mapping for the parametric weak vector variational inequality is discussed. As applications, Lipschitzian
continuity and differentiability of the solution mapping are also investigated for a parametric variational inequality. 相似文献
4.
Suppose that d≥1 is an integer, α∈(0,d) is a fixed parameter and let I α be the fractional integral operator associated with d-dimensional Walsh-Fourier series on (0,1] d . Let p, q be arbitrary numbers satisfying the conditions 1≤p<d/α and 1/q=1/p?α/d. We determine the optimal constant K, which depends on α, d and p, such that for any f∈L p ((0,1] d ) we have In fact, we shall prove this inequality in the more general context of probability spaces equipped with a regular tree-like structures. This allows us to obtain this result also for non-integer dimension. The proof exploits a certain modification of the so-called Bellman function method and appropriate interpolation-type arguments. We also present a sharp weighted weak-type bound for I α , which can be regarded as a version of the Muckenhoupt-Wheeden conjecture for fractional integral operators.
相似文献
$$ ||I_{\alpha } f||_{L^{q,\infty }((0,1]^{d})}\leq K||f||_{L^{p}((0,1]^{d})}. $$
5.
§ 1.Preliminary LetEbeareflexiveBanachspacewithanorm‖·‖ ,E′itsdualspaceand〈· ,·〉thepairbetweenE′andE .SupposethatHisaHilbertspacewiththenorm |·|andinnerproduct (· ,·)suchthatE H E′ ,( 1°)wheretheformersaredenseinthelattersandthecorrespondingidenticalmapsarecont… 相似文献
6.
Eleftherios N. Nikolidakis 《Journal of Fourier Analysis and Applications》2013,19(1):115-139
We obtain sharp estimates for the localized distribution function of $\mathcal{M}\phi $ , when ? belongs to L p,∞ where $\mathcal{M}$ is the dyadic maximal operator. We obtain these estimates given the L 1 and L q norm, q<p and certain weak-L p conditions.In this way we refine the known weak (1,1) type inequality for the dyadic maximal operator. As a consequence we prove that the inequality 0.1 is sharp allowing every possible value for the L 1 and the L q norm for a fixed q such that 1<q<p, where ∥?∥ p,∞ is the usual quasi norm on L p,∞. 相似文献
7.
Yair Censor Aviv Gibali Simeon Reich Shoham Sabach 《Set-Valued and Variational Analysis》2012,20(2):229-247
We study the new variational inequality problem, called the Common Solutions to Variational Inequalities Problem (CSVIP).
This problem consists of finding common solutions to a system of unrelated variational inequalities corresponding to set-valued
mappings in Hilbert space. We present an iterative procedure for solving this problem and establish its strong convergence.
Relations with other problems of solving systems of variational inequalities, both old and new, are discussed as well. 相似文献
8.
Xiting Liang 《偏微分方程(英文版)》1995,8(2):145-158
The regularity for solutions of elliptic equations is rather perfectly solved. But it does not so perfect for that of elliptic variational inequalities. In literature only different special situations are considered. Now the boundedness, C^{0,λ} continuity and C^{1,α} regularity are proved for solutions of one-sided obstacle problems under more general structural conditions, in which the growth orders of u are permitted to reach the critical exponents and the growth order ϒ of the gradient in D is permitted to be super critical as 1 < p < n. 相似文献
9.
Boundedness of Solutions for Elliptic Variational InequalitiesBoundednessofSolutionsforEllipticVariationalInequalities¥YeRuif... 相似文献
10.
M. Golestani H. Sadeghi Y. Tavan 《Journal of Optimization Theory and Applications》2018,179(3):896-916
In this paper, a multiobjective problem with a feasible set defined by inequality, equality and set constraints is considered, where the objective and constraint functions are locally Lipschitz. Here, a generalized Stampacchia vector variational inequality is formulated as a tool to characterize quasi- or weak quasi-efficient points. By using two new classes of generalized convexity functions, under suitable constraint qualifications, the equivalence between Kuhn–Tucker vector critical points, solutions to the multiobjective problem and solutions to the generalized Stampacchia vector variational inequality in both weak and strong forms will be proved. 相似文献
11.
黄龙光 《数学物理学报(A辑)》2009,29(1):114-120
建立Hausdorff拓扑向量空间的非空凸子集到其值域为连续线性映射空间L(X, Y) 内的C -单调映射的弱向量变分不等式和它的纯量型变分不等式问题解的存在性, 讨论该弱向量变分不等式与之相联系的纯量型变分不等式解集的关系, 利用映射的C -弱次连续和C -单调性及其集值映射的不动点定理,通过纯量型变分不等式解集所诱导的集值映射所具有的特性给出弱向量变分不等式解集的连通性. 相似文献
12.
13.
Szilárd László 《Journal of Optimization Theory and Applications》2011,150(3):425-443
In this paper, we introduce a new class of operators. We present some fundamental properties of the operators belonging to
this class and, as applications, we establish some existence results of the solutions for several general variational inequalities
involving elements belonging to this class. 相似文献
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16.
In this note we give an existence result to a class of variational inequalities associated with quasilinear elliptic operators of second order with lower order terms. We prove “a priori” estimate by an extension of the truncation method to the nonlinear case. 相似文献
17.
渐近非扩张映射变分不等式的不动点解 总被引:1,自引:0,他引:1
设X是实的Banach空间且有一致Gateaux可微范数和一致正规结构,C是X的非空闭凸子集,T,f分别是C上的渐近非扩张映射与压缩映射,X0∈C,xn+1=anT^mXn+(1-an)f(xn),n=0,1,2,…,当an∈(O,1)满足适当条件时,则{Xn)强收敛到某变分不等式的不动点解. 相似文献
18.
P. Falsaperla 《Numerical Functional Analysis & Optimization》2014,35(7-9):1018-1042
We consider a class of parametric variational inequalities where both the operator and the convex set depend on time. This kind of variational inequalities are useful to model many time dependent equilibrium problems. We study the Lipschitz continuity of the solutions with respect to the time parameter and construct approximations for them which minimize the average worst case error. Some improved estimates of the Lipschitz constant for this class of problems are given. In order to illustrate our procedure, we study a classical network equilibrium problem. 相似文献
19.
In this paper, we study a class of implicit vector variational inequalities which contain implicit variational inequalities and generalized quasivariational inequalities as special cases. By employing the Fan–Kakutani fixed-point theorem and the Oettli scalarization procedure, respectively, we establish several existence results for implicit vector variational inequalities. 相似文献
20.
We use the concept of Fréchet approximate Jacobian matrices to establish the local uniqueness of solutions to general variational inequalities which involve continuous, not necessarily locally Lipschitz continuous data. 相似文献