A NOTE ON WEIGHTED SOBOLEV SPACES RELATED TO WEAKLY AND STRONGLY DEGENERATE DIFFERENTIAL OPERATORS

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.

Keywords

• degenerate equation
• weighted sobolev spaces
• poincar´e’s inequality