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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

A remark on the regularity of the div-curl system

Author(s): Irina Mitrea; Marius Mitrea
Journal: Proc. Amer. Math. Soc. 137 (2009), 1729-1733.
MSC (2000): Primary 35B65, 58A10; Secondary 35F05, 42B20
Posted: November 4, 2008
MathSciNet review: 2470831
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Abstract | References | Similar articles | Additional information

Abstract: As a limiting case of the classical Calderón-Zygmund theory, in this note we study the Besov regularity of differential forms $ u$ for which $ du$ and $ \delta u$ have absolutely integrable coefficients in $ {\mathbb{R}}^n$.

References:

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J.Bourgain and H.R.Brezis, On the equation $ {\text div}\,Y=f$ and application to control of phases, J. Amer. Math. Soc., 16 (2003), no.2, 393-426. MR 1949165 (2004d:35032)

2.
L.Lanzani and E.M.Stein, A note on div curl inequalities, Math. Res. Lett., 12 (2005), no.1, 57-61. MR 2122730 (2005m:58001)

3.
J.Van Schaftingen, Estimates for $ L^1$-vector fields, C. R. Math. Acad. Sci. Paris, 339 (2004), no.3, 181-186. MR 2078071 (2005b:35018)

4.
H.Triebel, Interpolation Theory, Function Spaces, Differential Operators, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978. MR 500580 (80i:46032a)

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Additional Information:

Irina Mitrea
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
Email: im3p@virginia.edu

Marius Mitrea
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: marius@math.missouri.edu

DOI: 10.1090/S0002-9939-08-09671-8
PII: S 0002-9939(08)09671-8
Keywords: Differential forms, div-curl system, Besov spaces, regularity, embeddings
Received by editor(s): June 3, 2008
Posted: November 4, 2008
Additional Notes: The first author was partially supported by NSF grant DMS-0547944
The second author was partially supported by NSF grants DMS-90400639 and DMS-FRG-0456306
Communicated by: Michael T. Lacey
Copyright of article: Copyright 2008, American Mathematical Society




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