We show that the limit infimum, as time $\,t\,$ goes to infinity, of any uniformly bounded in $H^{3/2+}\cap L^1$ solution intermediate long wave (ILW) equation converges zero locally...

Suppose that C is a nonempty closed convex subset of a real uniformly convex Banach space X . Let T : C→ C be an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover, we prove that if T is uniformly L-Lipschitzian and completely continuous, then the iterative scheme converges strongly to some fixed point...

Let E be an elliptic curve over the rationals. L infinite Galois extension of rationals with uniformly bounded local degrees at almost all primes. We will consider L(E_tor) where we adjoin coordinates torsion points E. In this paper prove effective lower bound for height non-zero elements in that are not a root unity.

in this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regularasymptotically nonexpansive mappings in a real reflexive banach space with a uniformly g$hat{a}$teaux differentiable norm. our result is applicable in $l_{p}(ell_{p})$ spaces,$1 < p

We prove that a general system of variational difference equations is uniformly exponentially stable if and only if certain associated sets are of the second category. We also deduce necessary and sufficient conditions for uniform exponential stability of systems with uniformly bounded coefficients. We apply our results for the study of exponential stability of linear skew-product flows, genera...

In this article, we will consider second order uniformly elliptic operators of divergence form defined on Rn with measurable coefficients. Mainly, we will give estimates on the dimension of space of solutions that grow at most polynomially of degree d. More precisely, in terms of a rectangular coordinate system {x1, . . . , xn}, a second order uniformly elliptic operator of divergence form, L, ...

Abstract. We study distribution of orbits of a lattice Γ ⊆ SL(n,R) in the the space Vn,l of l-frames in R (1 ≤ l ≤ n − 1). Examples of dense Γ-orbits are known from the work of Dani, Raghavan, and Veech. We show that dense orbits of Γ are uniformly distributed in Vn,l with respect to an explicitly described measure. We also establish analogous result for lattices in Sp(n,R) that act on the spac...

Let L be a symmetric second order uniformly elliptic operator in divergence form acting in a bounded Lipschitz domain Ω of RN and having Lipschitz coefficients in Ω. It is shown that the Rellich formula with respect to Ω and L extends to all functions in the domain D = {u ∈ H1 0 (Ω); L(u) ∈ L2(Ω)} of L. This answers a question of A. Chäıra and G. Lebeau.

I fhI is the respective Haar coefficient, and σ(I) = ±1. This operator, which we denote by Tσ, is a dyadic martingale transform. The martingale transform is bounded as an operator on L(R,C). We want to find a condition on matrix weights, U and V , that implies that all martingale transforms are uniformly bounded as operators from L(R,C, V ) to L(R,C, U) where L(R,C, V ) is the space of function...

We obtainC2,β estimates up to the boundary for solutions to degenerate Monge–Ampère equations of the type det D2u = f in , f ∼ distα(·, ∂ ) near ∂ , α > 0. As a consequence we obtain global C∞ estimates up to the boundary for the eigenfunctions of the Monge–Ampère operator (det D2u)1/n on smooth, bounded, uniformly convex domains in Rn .