Poincaré-type inequalities in Musielak spaces

Youssef Ahmida, Ahmed Youssfi
2019 Annales Academiae Scientiarum Fennicae: Mathematica  
In this paper we investigate Poincaré-type integral inequalities in the functional Musielak structure. We extend the ones already well known in Sobolev, Orlicz and variable exponent Sobolev spaces. We introduce conditions on the Musielak functions under which they hold. The identification with null trace functions space is given. to hold for every u ∈ W m 0 L M (Ω) where c > 0 is a constant. We also get the same inequality in the subspace W m 0 E M (Ω) under minimal assumptions.
doi:10.5186/aasfm.2019.4468 fatcat:56mbxmrfo5fjzhgizhthxitdvy