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61.
In this paper we prove a quantitative form of Landis’ conjecture in the plane. Precisely, let W(z) be a measurable real vector-valued function and V(z) ≥0 be a real measurable scalar function, satisfying ‖W‖ L ∞(R 2) ≤ 1 and ‖V‖ L ∞(R 2) ≤ 1. Let u be a real solution of Δu ? ?(Wu) ? Vu = 0 in R 2. Assume that u(0) = 1 and |u(z)| ≤exp (C 0|z|). Then u satisfies inf |z 0| =R sup |z?z 0| <1|u(z)| ≥exp (?CRlog R), where C depends on C 0. In addition to the case of the whole plane, we also establish a quantitative form of Landis’ conjecture defined in an exterior domain. 相似文献
62.
In the present paper, we introduce some new subclasses of meromorphic starlike,convex, close-to-convex and quasi-convex functions of β-reciprocal in terms of the linear operator using subordination. We obtain the coefficient estimates, convolution properties, integral preserving properties and inclusion relationships of the classes. The results presented here include several results as their special cases. 相似文献
63.
This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group H n. The sharp bounds for the strong type(p, p)(1 ≤ p ≤∞) estimates of n-dimensional Hausdorff operators on H n are obtained. The sharp bounds for strong(p, p) estimates are further extended to multilinear cases. As an application, we derive the sharp constant for the multilinear Hardy operator on H n. The weak type(p, p)(1 ≤ p ≤∞) estimates are also obtained. 相似文献
64.
A local parallel superconvergence method for the incompressible flow by coarsening projection 下载免费PDF全文
In this article, we investigate a local parallel superconvergence method by coarsening projection for the incompressible Stokes flow. The method is a combination of the local superconvergence technique and the given framework of local parallel method. For the smooth subdomains, the local superconvergence method is applied in a higher order finite dimensional space corresponding to an appropriate coarse mesh on interior domain. Moreover, a useful and flexible local parallel method is designed to obtain the local parallel superconvergence results of presented method, which offset theoretical limitation of the model without the smoothness of the exact solution and a priori regularity of the underlying problem over the whole domain. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1209–1223, 2015 相似文献
65.
Let L be an elliptic operator, we give arguments about the duality estimate between Morrey spaces and its pre-dual spaces characterized by the heat kernel associated to L that is given in [6],[8]. 相似文献
66.
For the coupled system with moving boundary values of multilayer dynamicsof fluids in porous media,a characteristic finite difference fractional step scheme appli-cable to the parallel arithmetic is put forward.Some techniques,such as the change ofregions,the calculus of variations,the piecewise threefold quadratic interpolation,themultiplicative commutation rule of difference operators,the decomposition of high orderdifference operators,and the prior estimates,are adopted.The optimal order estimatesin the l2norm are derived to determine the error in the approximate solution.This nu-merical method has been successfully used to simulate the flow of migration-accumulationof the multilayer percolation coupled system.Some numerical results are well illustratedin this paper. 相似文献
67.
The penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions is investigated in this paper. Since this class of nonlinear slip boundary conditions include the subdifferential property, the weak variational formulation is a variational inequality problem of the second kind. Using the penalty finite element approximation, we obtain optimal error estimates between the exact solution and the finite element approximation solution. Finally, we show the numerical results which are in full agreement with the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
68.
69.
We consider a Cauchy problem for the modified Helmholtz equation. A conditional stability estimate is proved. Two order optimal regularization methods and error estimates are investigated. Numerical experiment shows that these methods work well. 相似文献
70.