Sentence examples for regularity estimate from inspiring English sources

Since, the elliptic regularity estimate [10, Lemma ] yields (4.11).

Our purpose in this paper is to extend local regularity estimate in [6] to global regularity estimates, assuming that.

More specifically, we start by extending a classical regularity estimate for the H1-norm of the divergence of the displacement field to the heterogeneous case.

Since X ∈ L 2 ( Q T ), it follows from the elliptic regularity estimate [[7], Lemma 2.3] that ∫ Q T | X x i x j | 2 d x d t ≤ m 3, i, j = 1, …, n.

By the idea of Shen [1], Guo, Li, and Peng [9] obtained a regularity estimate of the kernel (R_{L}) and proved the commutators ([b, R_{L}]) are bounded on some Lebesgue spaces (L^{p}) with (bin operatorname{BMO}(mathbb{R}^{n})).

We also have the regularity estimates for the solution ( ρ, u ) to FBVP (3.2) as follows.

We show the global regularity estimates for the following parabolic polyharmonic equation in under proper conditions.

In this section, we derive the higher-order regularity estimates of the solutions.

We obtain sharp geometric regularity estimates for solutions along the boundary of plateaus sets.

Our results extend the existing regularity estimates in Lebesgue spaces to weighted Orlicz spaces.

As applications of the regularity estimates, we establish asymptotic expansions for fundamental solutions.