Weakly symmetric pseudo-Riemannian manifoldsWe study rates of convergence of solutions in L 2 and H 1/2 for a family of elliptic systems $${\\{\\mathcal{L}_\\varepsilon\\}}$$ with rapidly oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a ...
Let (dn) be a weakly null mds in LF . Let ε > 0. For any M > 0 let en = dn ·χ ,[|dn|≤M] e˜n = dn ·χ[|dn|>M] and for n ≥ 2 let fn = IE(en|d1, . . . , dn−1). Notice that (en − fn) is a mds, uniformly bounded by 2M and hence in L2...
This implies that {xn} converges weakly to q. The proof of Theorem 1 is completed. 2 Proof of Theorem 2. Taking γn = 0, ∀n 1, and βn = 1 − αn, ∀n 1, in Theorem 1, then the conclusion of Theorem 2 can be obtained from Theorem 1 immediately. 2 Proof of Theorem ...
weakly-quasi-first-countablesigma-compact frontierWe consider the numerical solution of the first-order-system version of the Tricomi problem. A new Galerkin method, using differing spaces of test and trial functions, is presented. We show that the error in the L2 norm is O(hk) if finite ...
Less conserved regions, such as the glycan cap and mucin-like domain (MLD), can also be targeted by protective antibodies and typically represent the largest antibody responses found in survivors; however, such antibodies are usually weakly or non-neutralizing and species specific (Murin et al.,...
cation: 35L15, 60Fxx, 60Gxx, 82Bxx 1 Partially supported by the research grant of RFBR (06-01-00086) 1 Introduction The paper concerns problems of long-time convergence to an equilibrium distribution in a coupled system. We have proved the convergence for partial differential equations of ...
Therefore, there exists a subsequence {unk } in BV ( ) that converges strongly in L1( ) to some u∗ ∈ BV ( ) as k →∞, while {Dunk } converges weakly as a measure to Du∗. Since K is linear and continuous, {K unk } converges strongly to K u∗ in L2( ). By the ...
Yunxia Wei and Yanping Chen, Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions, Advances in Applied Mathematics and Mechanics, 4(1) (2012), 1-20.Wei, Y., Chen, Y.: Convergence analysis of the spectral methods for ...
Oliveira, P.E., Suquet, Ch. (1995), L2[0, 1] weak convergence of the empirical process for de- pendent variables, in: Wavelets and Statistic (A. Antoniadis and G. Oppenheim, eds.), Lecture Notes in Statistics, 103, 331-344.
under suitable assumptions on their covariance structure (see Louhichi [7] and Oliveira and Suquet =-=[11, 12]-=- for the best known results on the covariance decrease rates for the convergence in D[0, 1], L2[0, 1] or Lp[0, 1], respectively), Zn converges weakly to a centered ...