Interpolation inequalities for derivatives in variable exponent Lebesgue–Sobolev spaces

Gagliardo–Nirenberg type inequality for variable exponent Lebesgue spaces

“…In case p(·) = q(·) and 1 < p − p + < ∞ Theorem 1.1 was proved by Zang and Fu in [20]. The method of our proof is based on the well known pointwise multiplicative inequalities for derivatives and on some properties of CalderonLozanovskii interpolation spaces.…”

“…Recently, the Gagliardo-Nirenberg inequalities have been sharpened and extended in different directions. In particular, we mention the works [1,9,10,19,20]. Note that, interpolation inequalities in a more general form than (1.1) with other norms…”

Existence of three solutions for variable exponent elliptic systems

“…According to [16], the norm |.| 2, p(x) is equivalent to the norm | .| p(x) in the space [2]) For p, r ∈ C + ( ) such that r (x) < p * * (x) for all x ∈ , there is a continuous and compact embedding…”

EXISTENCE OF THREE SOLUTIONS FOR A NAVIER BOUNDARY VALUE PROBLEM INVOLVING THE p(x)-BIHARMONIC

“…Remark 2.1. According to [14], u W 2,p(x) (Ω) is equivalent to |△u| p(x) in X. Consequently, the norms u W 2,p(x) (Ω) and u are equivalent.…”