Some non-standard Sobolev spaces, interpolation and its application to PDE

Abstract

We consider some nonstandard Sobolev spaces in one dimension, in which functions have different regularity in different subsets. Those spaces are useful in the study of some nonlinear elliptic and parabolic equations where the nonlinearity is highly degenerate and, in order to handle this degeneracy, additional partial regularity in subsets is required. The authors give denseness and interpolation results that are needed for the PDE theory to apply