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Subelliptic mollifiers and a basic pointwise estimate of Poincaré type. (English) Zbl 0893.35023
The paper proves a pointwise estimate which has many remarkable applications in the analysis of PDEs. By means of an elementary argument involving a family of mollifiers taylored on the subelliptic geometry, the authors characterize domains supporting the Poincaré inequality or the compact embedding and derive the proof of the pointwise estimate.

MSC:
35J15 Second-order elliptic equations
26D10 Inequalities involving derivatives and differential and integral operators
35A30 Geometric theory, characteristics, transformations in context of PDEs
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