Generalization of Poincar ´e inequality in a Sobolev Space with exponent constant to the case of Sobolev space with a variable exponent

Moulay Rchid Sidi Ammi , Ibrahim Dahi

In this work, we study the Poincare inequality in Sobolev spaces with variable exponent. As a consequence of this ´ result we show the equivalent norms over such cones. The approach we adopt in this work avoids the difficulty arising from the possible lack of density of the space C∞ 0 (Ω).