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Levi's parametrix for some sub-elliptic non-divergence form operators
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Levi's parametrix for some sub-elliptic non-divergence form operators
Andrea Bonfiglioli, Ermanno Lanconelli, and Francesco Uguzzoni
Abstract.
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, Universitŕ 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, Universitŕ 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, Universitŕ 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.
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