Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896597 | Journal of Functional Analysis | 2018 | 27 Pages |
Abstract
In this paper, we characterize all the distributions FâDâ²(U) such that there exists a continuous weak solution vâC(U,Cn) (with UâΩ) to the divergence-type equationL1âv1+...+Lnâvn=F, where {L1,â¦,Ln} is an elliptic system of linearly independent vector fields with smooth complex coefficients defined on ΩâRN. In case where (L1,â¦,Ln) is the usual gradient field on RN, we recover the classical result for the divergence equation proved by T. De Pauw and W. Pfeffer. Its proof is based on the closed range theorem and inspired by [3] and [6] in the classical case. Our method slightly differs from theirs by relying on the Banach-Grothendieck theorem and introducing tools from pseudodifferential operators, useful in our local setting of a system of complex vector fields with variable coefficients.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Laurent Moonens, Tiago Picon,