Sentence examples for obtained regularity from inspiring English sources

Zhou and Gala [20] obtained regularity criteria of solutions in term of and in the multiplier spaces.

Boccardo and Gallouët [6, 7] obtained,, regularity for weak solutions of the problem with some structural conditions.

Recently, Byun and Wang [8] obtained,, regularity for weak solutions of the general nonlinear elliptic problem (1.10).

In particular, Abdellaoui et al. [12] obtained regularity of solutions to the following nonlocal nonlinear problem: textstylebegin{cases} (-Delta)^{s} u-lambdafrac{u}{|x|^{2s}}=f(x),&x inOmega, u>0, &xinOmega, u=0, & xinmathbb{R}^{N}setminusOmega, end{cases} (1.3) with (fin L^{m}(Omega)) and (0

For the n-switching problem we obtain regularity results for the solutions of the variational inequalities.

We also obtain regularity properties, both for the solution and for its free boundary.

The book collects many techniques that are helpul in obtaining regularity results for solutions of nonlinear systems of partial differential equations.

Corollaries 2.6 and 3.2 can be applied to obtain regularity for (3.10).

In [13], the authors gave sufficient conditions on the kinematics pressure in order to obtain regularity and uniqueness of the weak solutions to the micropolar fluid equations.

The local indices vi and vj denote the degree to which a cell must receive or deliver individuals in order to obtain regularity.

Wu [1], [2] obtained some regularity criteria only relying on the velocity u.