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Levi's parametrix for some sub-elliptic non-divergence form operators


Authors: Andrea Bonfiglioli, Ermanno Lanconelli and Francesco Uguzzoni
Journal: Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 10-18
MSC (2000): Primary 35A08, 35H20, 43A80; Secondary 35A17, 35J70
DOI: https://doi.org/10.1090/S1079-6762-03-00107-0
Published electronically: January 31, 2003
MathSciNet review: 1988867
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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 Hörmander vector fields and $a_{i,j}$ are Hölder continuous functions belonging to a suitable class of ellipticity.


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Additional Information

Andrea Bonfiglioli
Affiliation: Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
Email: bonfigli@dm.unibo.it

Ermanno Lanconelli
Affiliation: Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
Email: lanconel@dm.unibo.it

Francesco Uguzzoni
Affiliation: Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
Email: uguzzoni@dm.unibo.it

DOI: https://doi.org/10.1090/S1079-6762-03-00107-0
Keywords: Non-divergence sub-elliptic operators, stratified groups, fundamental solutions, parametrix method
Received by editor(s): November 11, 2002
Published electronically: January 31, 2003
Additional Notes: Investigation supported by the University of Bologna Funds for selected research topics.
Communicated by: Michael Taylor
Article copyright: © Copyright 2003 American Mathematical Society

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