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On the regularity of vector fields underlying a degenerate-elliptic PDE


Authors: Erika Battaglia, Stefano Biagi and Giulio Tralli
Journal: Proc. Amer. Math. Soc. 146 (2018), 1651-1664
MSC (2010): Primary 35J70, 15A23, 47A56
DOI: https://doi.org/10.1090/proc/13866
Published electronically: November 13, 2017
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Abstract: In this note we discuss the relationship, under an algebraic constant rank condition, between the regularity of the characteristic form's coefficients of a degenerate elliptic linear PDO in $ \mathbb{R}^N$ and the regularity of vector fields controlling its degeneracy. We consider both the cases where the number of vector fields is $ N$ and it is equal to the rank.


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Additional Information

Erika Battaglia
Affiliation: Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato, 5 - 40126 Bologna, Italy
Address at time of publication: Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Via Trieste 63, 35121 Padova, Italy
Email: erika.battaglia@math.unipd.it

Stefano Biagi
Affiliation: Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato, 5 - 40126 Bologna, Italy
Email: stefano.biagi3@unibo.it

Giulio Tralli
Affiliation: Dipartimento di Matematica, Sapienza Università di Roma, P.le Aldo Moro 5, 00185 Roma, Italy
Email: tralli@mat.uniroma1.it

DOI: https://doi.org/10.1090/proc/13866
Keywords: Degenerate-elliptic operators, nonsmooth vector fields, constant rank quadratic forms.
Received by editor(s): January 28, 2016
Received by editor(s) in revised form: June 3, 2017
Published electronically: November 13, 2017
Additional Notes: The third author is the corresponding author
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2017 American Mathematical Society

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