1. An embedding theorem for sobolev spaces related to non-smooth vector fieldsand harnack inequality
- Author
-
Bruno Franchi and Ermanno Lanconelli
- Subjects
Sobolev space ,Harnack's principle ,Applied Mathematics ,Degenerate energy levels ,Mathematical analysis ,Order (group theory) ,Embedding ,Vector field ,Analysis ,Mathematics ,Harnack's inequality ,Sobolev inequality - Abstract
In the first part of this paper we study some differentiabilityperties properties (In Sobolev space setting)of functions belonging to thespace generated by the vector fields in aJ J Dx.connected open subset of Rn ; here the λjs are continuous (but in generalnot smooth) and nonnegative. In particular, under suitable geometricalhypotheses involving the integral curves of we get thenfollowing embedding estimate: for all test functions u and for suitable positive constants e and CP depending only on the "order of degeneration" of the vector fields Such a problem arises naturally in study of the pointewise estimates for the weak solutions of some degenerate elliptic equations with measurable coefficients.
- Published
- 1984