lower boundedness
Recently Published Documents


TOTAL DOCUMENTS

8
(FIVE YEARS 0)

H-INDEX

5
(FIVE YEARS 0)

2020 ◽  
Vol 18 (1) ◽  
pp. 1150-1163
Author(s):  
Abimbola Abolarinwa ◽  
Nathaniel K. Oladejo ◽  
Sulyman O. Salawu

Abstract This paper derives elliptic gradient estimates for positive solutions to a nonlinear parabolic equation defined on a complete weighted Riemannian manifold. Applications of these estimates yield Liouville-type theorem, parabolic Harnack inequalities and bounds on weighted heat kernel on the lower boundedness assumption for Bakry-Émery curvature tensor.


2016 ◽  
Vol 13 (04) ◽  
pp. 1641007 ◽  
Author(s):  
Meng Chen ◽  
Ming Li ◽  
G. R. Liu

This paper represents some basic mathematic theories for G[Formula: see text] spaces of functions that can be used for weakened weak (W2) formulations, upon which the smoothed finite element methods (S-FEMs) and the smoothed point interpolation methods (S-PIMs) are based for solving mechanics problems. We first introduce and prove properties of G[Formula: see text] spaces, such as the lower boundedness and convergence of the norms, which are in contrast with H1spaces. We then prove the equivalence of the Gsnorms and its corresponding semi-norms. These mathematic theories are important and essential for the establishment of theoretical frame and the development of relevant numerical approaches. Finally, numerical examples are presented by using typical S-FEM models known as the NS-FEM and [Formula: see text]S-FEM to examine the properties of a smoothed method based on Gsspaces, in comparison with the standard FEM with weak formulation.


2005 ◽  
Vol 57 (3) ◽  
pp. 506-534 ◽  
Author(s):  
Leonard Gross ◽  
Martin Grothaus

AbstractContractivity and hypercontractivity properties of semigroups are now well understood when the generator, A, is a Dirichlet form operator. It has been shown that in some holomorphic function spaces the semigroup operators, e−tA, can be bounded below from Lp to Lq when p, q and t are suitably related. We will show that such lower boundedness occurs also in spaces of subharmonic functions.


2002 ◽  
Vol 3 (1) ◽  
pp. 91 ◽  
Author(s):  
Salvador Romaguera ◽  
M.P. Schellekens

<p>The complexity (quasi-metric) space was introduced in [23] to study complexity analysis of programs. Recently, it was introduced in [22] the dual complexity (quasi-metric) space, as a subspace of the function space [0,) <sup>ω</sup>. Several quasi-metric properties of the complexity space were obtained via the analysis of its dual.</p> <p>We here show that the structure of a quasi-normed semilinear space provides a suitable setting to carry out an analysis of the dual complexity space. We show that if (E,) is a biBanach space (i.e., a quasi-normed space whose induced quasi-metric is bicomplete), then the function space (B*<sub>E</sub>, <sub>B*</sub> ) is biBanach, where B*<sub>E</sub> = {f :   E  Σ<sup>∞</sup><sub>n=0</sub> 2<sup>-n</sup>( V ) }  and <sub>B*</sub> = Σ<sup>∞</sup><sub>n=0</sub> 2<sup>-n</sup> We deduce that the dual complexity space admits a structure of quasinormed semlinear space such that the induced quasi-metric space is order-convex, upper weightable and Smyth complete, not only in the case that this dual is a subspace of [0,)<sup>ω</sup> but also in the general case that it is a subspace of F<sup>ω</sup> where F is any biBanach normweightable space. We also prove that for a large class of dual complexity (sub)spaces, lower boundedness implies total boundedness. Finally, we investigate completeness of the quasi-metric of uniform convergence and of the Hausdorff quasi-pseudo-metric for the dual complexity space, in the context of function spaces and hyperspaces, respectively.</p>


1992 ◽  
Vol 121 (3-4) ◽  
pp. 245-252 ◽  
Author(s):  
T. Domínguez Benavides ◽  
G. López Acedo

SynopsisUsing some new expressions for the weakly convergent sequences coefficient WCS(X) the lower boundednessis proved, where δ(-) is the (Clarkson) modulus of convexity. We also define a modulus of noncompact convexity concerning nearly uniformly convex spaces which is used to obtain another lower bound for WCS(X). The computation of this modulus in Ip-spaces shows that our second lower bound is the best possible in these spaces.


Sign in / Sign up

Export Citation Format

Share Document