Sentence examples for higher regularity of from inspiring English sources

In order to obtain higher regularity of global solutions, there are many complicated estimates on higher derivations of solutions to be involved, this is our main difficulty.

Now, we end this section with the following lemma, which plays an important role in the proof of higher regularity of the pullback attractors.

In fact, the better inclusion between Morrey and Hölder spaces permits to obtain higher regularity of the solutions to different elliptic and parabolic boundary problems.

In order to obtain a higher regularity of global strong solutions, there are many complicated estimates on higher derivations of the solution involved; this is our difficulty.

Before we dwell into a review of results concerning higher regularity of the classifying maps, we consider in the next section the basic examples of projective varieties that are classifying spaces.

Due to the solution of the corresponding stationary equation of (1.1) (-Delta h+lambda h+f(h)=g) only belonging to (H^{1}), we cannot expect any higher regularity of the global attractor than (mathcal {H}).

This is due to the fact that the angle entropy of the buried residues is lower than that of the exposed ones, demonstrating the higher regularities of the protein fragments in core regions.

The continuity and curvature terms need to be weighted with values just high enough to maintain a high regularity of the mesh.

Moreover, due to the strong-coupling property of the k-ε equations, we need a corresponding high regularity of the unknown functions k and ε.

Stated simply, the high nonlinearity of the k-ε equations leads to the necessity of high regularity of some unknown functions and thus leads to much difficulties for the a priori estimates.

The justification for the above assumption is the following: The continuity and curvature terms need to be weighted with values just high enough to maintain a high regularity of the mesh.