Sentence examples for considering the regularity of from inspiring English sources

Considering the regularity of the problem, the asymptotic behavior of the two processes shall be the same, as we shall see in what follows.

Furthermore, considering the regularity of the level set function, we present an operator splitting method to update the level set function, which performs well in maintaining its smoothness and stability.

Then, considering the regularity of φ ̃ 1 in the region where φ ̃ 1 > 0, we can pass to the limit in the boundary condition for ( φ ^ 1 p 1 ) ξ 1 to obtain that - ( φ ̃ 1 p 1 ) ξ 1 ( 0 ) = φ ̃ 2 q 2 ( 0 ).

The relevance of considering the regularity of adolescents weighing or measuring practises and their opportunities for weighing and measuring themselves have previously been highlighted [ 7, 14].

In this paper, by employing tensor products of regularizing functions as in [7, 8], we consider the regularity of the solutions of (1.3) and prove in an elementary way that (1.3) can be reduced to the classical equation (1.1) of smooth functions.

In this paper we consider the regularity of solutions to nonlinear Schrödinger equations (NLS), i ∂tu + 12 Δu = F u, u), (t, x) ∈ R × Rn,u(0) = φ, x ∈ Rn, where F is a polynomial of degree p with complex coefficients.

For instance, Chae [5], Agélas [6], and Wu [7] considered the regularity of MHD equations, and Capone [8] and Fuchs [9] studied the stability bifurcation of MHD equations.

In general, when quasilinear or nonlinear equations are considered, the regularity of weak solutions has been investigated under various growth conditions on lower order terms.

Indeed, Sharapudinov [33] was the first person to consider the regularity of the exponent function (p(x)) with a local log-Hölder continuity, and from then it is the usual hypothesis for harmonic analysis and theory of PDEs.

Cao and Wu [14] considered the regularity of weak solutions in terms of the one component of the gradient of the pressure begin{aligned} partial_{3}piin L^{p}bigl(0,T;L^{q} bigl(mathbf{R}^{3}bigr) bigr) quadmbox{for } frac{2}{p}+ frac{3}{q}= frac{7}{4}, frac{12}{7}< q leqinfty.

To the best knowledge of the authors of this paper, this is the first time in the category of the Lorentz spaces to consider the regularity of variable exponent powers of the gradient of weak solution for variational inequalities under the weakest conditions on coefficients and boundaries.