Sentence examples for basic properties of variable from inspiring English sources

Next we recall some basic properties of variable exponent spaces of Clifford-valued functions.

We recall in what follows some definitions and basic properties of variable exponent Lebesgue and Sobolev spaces,, and.

First we recall some basic properties of variable exponent spaces and variable exponent Sobolev spaces where is a domain.

We first introduce some definitions and basic properties of the variable exponent Lebesgue space (L^{p cdot)}(Omega)) and the variable exponent Lebesgue-Sobolev space (W^{1,p cdot)}(Omega)).

To make a self-contained paper, we first recall some definitions and basic properties of the variable exponent Lebesgue spaces L p ( x ) and the variable exponent Lebesgue-Sobolev spaces W 1, p ( x ).

In this section, we recall some definitions and basic properties of the variable exponent Lebesgue spaces L p ( R N ) and the variable exponent Lebesgue-Sobolev spaces W 1, p ( R N ) which will be treated in the next sections.

To make a self-contained paper, we first recall some definitions and basic properties of the variable exponent Lebesgue spaces L p ( x ) ( R N ) and the variable exponent Lebesgue-Sobolev spaces W 1, p ( x ) ( R N ).

The basic properties of the variable exponent Lebesgue-Sobolev spaces can be found from [19, 20].

The basic properties of the variable exponent Lebesgue-Sobolev spaces can be found in [24, 25].

The basic properties of the variable exponent Lebesgue-Sobolev spaces, that is, when w ( x ) ≡ 1 can be found from [24].

We state some basic properties of the variable exponent Lebesgue-Sobolev spaces L p ( x ) and W 1, p ( x ) , where Ω ⊂ R N is a bounded domain (for details, see [21 24]).