Article type :

Original article

Author :

Peter Kogut,Olha Kupenko,Guenter Leugering,Yue Wang

Volume :

27

Issue :

2

Abstract :

In this paper we discuss some issues related to Poincar´e’s inequality for a special class of weighted Sobolev spaces. A common feature of these spaces is that they can be naturally associated with differential operators with variable diffusion coefficients that are not uniformly elliptic. We give a classification of these spaces in the 1-D case bases on a measure of degeneracy of the corresponding weight coefficient and study their key properties.