An embedding theorem for sobolev spaces related to non-smooth vector fieldsand harnack inequality
Authors:
- 1 January 1984
- journal article
- research article
- Published by Taylor & Francis in Communications in Partial Differential Equations
- Vol. 9 (13) , 1237-1264
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.Keywords
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