Sentence examples for weak continuity from inspiring English sources

Note that a continuous and affine map is weakly continuous, so the weak continuity of is not required as well.

For strongly local forms we show existence of a maximal intrinsic metric (under a weak continuity condition) and for Dirichlet forms with an absolutely continuous jump kernel we characterize intrinsic metrics by bounds on certain integrals.

By weak continuity of f, we get fy = y.

Weak continuity and tight values imply the continuity w.r.t.

Our first result holds under the weak continuity assumption.

S without the sequential weak continuity of the involved mappings.

According to Theorem 2.6, the norm-to-weak continuity is easily checked.

By the norm-to-weak continuity of (J^{-1}), we have, for each (igeq1), (eta_{m_{k}}^{(i)} rightharpoonup u^) as (ktoinfty).

Consequently, there is a renamed subsequence of { u k } such that u k ⇀ u in E. Hence, by the weak-to-weak continuity of I ′, we have 〈 I ′ ( u k ), v 〉 → 〈 I ′ ( u ), v 〉, ∀ v ∈ E. (2.24).

In [6], the author studied the existence of a weak solution of Cauchy problem (1) in reflexive Banach spaces equipped with the weak topology, and the author assumed a weak-weak continuity assumption on f.

The interelement C1 weak-continuity conditions can be satisfied.