@article{Harjulehto_Hästö_2004, title={A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces.}, volume={17}, url={https://revistas.ucm.es/index.php/REMA/article/view/REMA0404120129A}, DOI={10.5209/rev_REMA.2004.v17.n1.16790}, abstractNote={We study the Poincaré inequality in Sobolev spaces with variable exponent. Under a rather mild and sharp condition on the exponent p we show that the inequality holds. This condition is satisfied e. g. if the exponent p is continuous in the closure of a convex domain. We also give an essentially sharp condition for the exponent p as to when there exists an imbedding from the Sobolev space to the space of bounded functions.}, number={1}, journal={Revista Matemática Complutense}, author={Harjulehto, Petteri and Hästö, Peter}, year={2004}, month={jun.}, pages={129–146} }