Sentence examples for originally proven from inspiring English sources

} end{aligned}The main theorem in this setting (originally proven in [3]) relates absolutely continuous curves in (mathbb W_p) with solutions of the continuity equation: Let ((mu _t)_{tin [0,1]}) be an absolutely continuous curve in (mathbb W_p(Omega )) (for (p>1) and (Omega subset mathbb R^d) an open domain).

Like computers, 3-D printers originally proved their worth in the business sector, cost a fortune and were bulkier than a Kelvinator.

It was originally proved in [17].

The result in Lemma 2 was originally proved in [4].

This lemma was originally proved by Jia et al. [2].

Levinson [2] originally proved the inequality for functions (f: (0,2c) tomathbb{R}) such that (f"' geq0).

The result in Theorem 4 was originally proved in [30], albeit by a different method.

The characterization for the first fragment was originally proved by Cohen, Perrin, and Pin using sophisticated semigroup-theoretic techniques.

Note that the proof of Lemma 9 holds the following result originally proved in [6], Remark 10.

In this survey we will describe a result, originally proved in [18], showing that this is not the case.

Here we prove a Hardy-type inequality in the upper half-space which generalize an inequality originally proved by Maz'ya (Sobolev Spaces, Springer, Berlin, 1985, p. 99).