Sentence examples for order uniformly from inspiring English sources
The particular and important case of a second order uniformly elliptic equation is the Laplace equation.
It is known that solutions to second order uniformly elliptic and parabolic equations, either in divergence or nondivergence (general) form, are Hölder continuous and satisfy the interior Harnack inequality.
end{cases}displaystyle end{aligned} (1.1) Here (Q:=Omegatimes 0,T]), (partial{Q}:=partialOmegatimes (0,T]), in which Ω is a bounded domain in (mathbb {R}^{n}) with smooth boundary ∂Ω and (nablacdot(D x,t nabla)+mathbf {b} x,t cdotnabla:=mathcal {A}) is a second order uniformly elliptic operator which the coefficients are assumed to be smooth (say Hölder continuous).
First of all, we are not claiming that they have high weak order uniformly in the stepsize, and we have no such proof apart from in the linear case when the higher order is inherited directly from the underlying deterministic extrapolation methods.
In this section, existence of common fixed points of ordered C q -commuting and ordered uniformly C q -commuting mappings is established in hyperbolic ordered metric spaces by utilizing the notions of ordered S-contractions and ordered asymptotically S-nonexpansive mappings.
Farrell et al. [6] and Boglaev and Pack [7] employed first-order uniformly convergent difference schemes for singularly perturbed semilinear differential equations with a discontinuous source term.
Falco and O'Riordan [8] developed a second-order uniformly convergence numerical method on piecewise-uniform Shishkin meshes for a reaction-diffusion equation with a discontinuous diffusion coefficient.
We study positive C0-semigroups on Lp associated with second-order uniformly elliptic divergence-type operators with singular lower-order terms, subject to a wide class of boundary conditions.
ordered uniformly R-subweakly commuting [23] if there exists a real number R > 0 such that.
In both cases we saw our orders uniformly slow down across the fieldin technology in 2001, in financial services in 2007.
for all x ∈ Y. (5) ordered uniformly R-subweakly commuting [23] if there exists a real number R > 0 such that .
