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We construct the fundamental solutions for the sub-elliptic operators in non-divergence form ${\textstyle\sum_{i,j}} a_{i,j}(x,t)\,X_iX_j-\partial_t$ and ${\textstyle\sum_{i,j}}a_{i,j}(x)\,X_iX_j$, where the $X_i$'s form a stratified system of H\"ormander vector fields and $a_{i,j}$ are H\"older continuous functions belonging to a suitable class of ellipticity.

Copyright 2003 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 09 (2003), pp. 10-18
• Publisher Identifier: S 1079-6762(03)00107-0
• 2000 Mathematics Subject Classification. Primary 35A08, 35H20, 43A80; Secondary 35A17, 35J70
• Key words and phrases. Non-divergence sub-elliptic operators, stratified groups, fundamental solutions, parametrix method
• Received by editors November 11, 2002
• Posted on January 31, 2003
• Communicated by Michael Taylor
• Comments (When Available)

Andrea Bonfiglioli

Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy

E-mail address: bonfigli@dm.unibo.it

Ermanno Lanconelli

Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy

E-mail address: lanconel@dm.unibo.it

Francesco Uguzzoni

Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy

E-mail address: uguzzoni@dm.unibo.it

Investigation supported by the University of Bologna Funds for selected research topics.