Sentence examples for regularity of the solution from inspiring English sources

In the second step, regularization step, an H1 regularity of the solution is ensured while keeping the feasibility of solution with respect to the set of control constraints.

It is shown in  [15,16] that for sufficiently regular initial values the regularity of the solution to the KdV equation is not diminished as it is evolved in time (although this does not rule out the appearance of high frequency oscillations).

Now, let us study the regularity of the solution w.

Now we will prove the global regularity of the solution.

The key element is a sensor, which measures the local regularity of the solution.

The following theorem states the regularity of the solution of (2.7).

Then, using elliptic regularity and second order estimates, we can show the regularity of the solution.

end{cases} (2.9) Next, we will get the regularity of the solution (hat{u}(t)).

In Section 4 we show the Hölder regularity of the solution (u t, x)).

We establish several results on the regularity of the solutions.

Based on the boundedness, we can further study the regularity of the solutions.