For any n≥2, Ω⊂Rn, and given convex coercive Hamiltonian function H∈C0(Rn), we find an optimal sufficient condition on H, that is, for c∈R, the level set H−1(c) does not contain line segment, such then absolute minimizer u∈AMH(Ω) enjoys linear approximation property. As consequences, show when n=2, if u∈C1; u∈AMH(R2) satisfies a growth at infinity, u is R2. In particular, H strictly Banach norm...

In this note we offer a short, constructive proof for Hilbert spaces of Lindenstrauss’ famous result on the denseness of norm attaining operators. Specifically, we show given any A ∈ L(H) there is a sequence of rank-1 operators Kn such that A+Kn is norm attaining for each n and Kn converges in norm to zero. We then apply our construction to establish denseness results for norm attaining operato...

Abstract In this paper, we discuss a priori error estimates for the finite volume element approximation of optimal control problem governed by Stokes equations. Under some reasonable assumptions, obtain $L^{2}$ L 2 -norm estimates. The approximate orders state, costate,...

We analyze a new Galerkin finite element method for numerically solving a linear convection-dominated convection-diffusion problem in two dimensions. The method is shown to be convergent, uniformly in the perturbation i ii parameter, of order h ' in a global energy norm which is stronger than the L norm. This order is optimal in this norm for our choice of trial functions.

We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. A metric space X is said to have operator norm localization property if there exists 0 < c ≤ 1 such that for every r > 0, there is R > 0 for which, if ν is a positive locally finite Borel measure on X, H is a separable infinite dimensional Hilbert space and T is a bounded ...

A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple (L (2)(Ω)(2)) space replacing the complex H(div; Ω) space. Some a priori error estimates in L...

In [20] a symmetric interior penalty discontinuous Galerkin (DG) method was presented for the time-dependent wave equation. In particular, optimal a-priori error bounds in the energy norm and the L-norm were derived for the semi-discrete formulation. Here the error analysis is extended to the fully discrete numerical scheme, when a centered second-order finite difference approximation (“leapfro...

The poles/residues expression of the frequency-limited H2-norm is used to derive two upper bounds on the H∞-norm of a MIMO LTI dynamical system. These bounds can be efficiently computed when the eigenvalues and eigenvectors of the model are available. This specificity make them particularly well suited to watch the H∞-norm of the approximation error in the context of the frequency-limited H2 mo...

Multiplicative relations in the cohomology ring of a manifold impose constraints upon its stable systoles. Given a compact Riemannian manifold (X, g), its real homology H∗(X, R) is naturally endowed with the stable norm. Briefly, if h ∈ Hk(X, R) then the stable norm of h is the infimum of the Riemannian kvolumes of real cycles representing h. The stable k-systole is the minimum of the stable no...