Sentence examples for obtain regularity from inspiring English sources

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

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

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

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.

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

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.

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<lambda<Lambda_{N,s}), where (Lambda _{N,s}) appears in the Hardy inequality (1.2).

Using a simplified physical model that ignores 3D effects of the complete structure, we develop a novel inter-slice regularization strategy to obtain global regularity.

In their article Potthast and Graben also work with a different functional space by assuming more regularity for the connectivity function W and then obtain more regularity for their solutions.