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

Battaglia, Erika; Biagi, Stefano; Tralli, Giulio

doi:10.1090/proc/13866

On the regularity of vector fields underlying a degenerate-elliptic PDE
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Proc. Amer. Math. Soc. 146 (2018), 1651-1664 Request permission

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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