Sentence examples for bounded and convex domain from inspiring English sources

Let and,,, be a smooth differential form in a bounded and convex domain.

In this paper, we also assume that is a bounded and convex domain in.

Let,,, be a solution of the non-homogeneous -harmonic equation in a bounded and convex domain, let be Green's operator, and let be the homotopy operator.

In the present paper, we deal with the composition of carathéodory and homotopy operators for differential forms satisfying the A-harmonic equation in the bounded and convex domain.

where u ∈ D ′ ( E, ∧ l ), l = 0, 1, …, n − 1, is a differential form defined in a bounded and convex domain E, and p > 1 is a constant.

Lemma 2.2Let u ∈ L loc s ( D, ∧ l ), l = 1, 2, …, n, 1 < s < ∞, be a differential form in a bounded and convex domain D ⊂ R n, and letTbe the homotopy operator defined on differential forms.

for any bounded and convex -John domain, where (3.11).

First, we use Lemma 2.3 for the bounded and convex -John domain.

for any bounded and convex -John domain, where (3.2). and are constants, the fixed cube, the cubes, the constant appeared in Lemma 2.3, and is the center of.

Ω is a bounded, open and convex domain with a smooth boundary ∂Ω in (mathbb{R}^{m}).

for any bounded and convex δ-John domain Ω ∈ ℝ n.