Sentence examples for the energy functional from inspiring English sources

Define the energy functional (4.33).

Proposition 2. The energy functional is convex.

The energy functional of problem (1.2) is given by (22).

which is the Euler equation for the energy functional (1.5).

By (f3), the energy functional J is even.

The energy functional in (21) is convex, with global minimum.

Moreover, they derived decay estimate for the energy functional.

For convenience, we call the energy functional (6) as vector-valued C-V model.

Proof of Theorem 1.1 We know the energy functional I ( u ) is continuous and even.

In this section, we discuss the decay rates of the energy functional associated with problem (1.6).

Then the energy functional (J_{lambda}) is coercive and bounded below on (mathcal{N}).