Estimating the gradient of vector fields via div and curl in variable exponent Sobolev spaces

We show an estimate of the gradient of vector fields u in terms of div u and curl u in vector-valued variable exponent Sobolev spaces with vanishing normal component on the boundary in simply connected 3D-domains.

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Bibliographic Details
Published in:Nonlinear analysis 2020-03, Vol.192, p.111666, Article 111666
Main Authors: Sin, Cholmin, Ri, Sin-Il
Format: Article
Language:English
Subjects:
Calderon–Zygmund operator
Div–curl system
Fields (mathematics)
Sobolev space
Variable exponent
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Description
Summary:We show an estimate of the gradient of vector fields u in terms of div u and curl u in vector-valued variable exponent Sobolev spaces with vanishing normal component on the boundary in simply connected 3D-domains.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2019.111666