A remark on the regularity of the div-curl system. (English) Zbl 1168.35325
Summary: 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 \( {\mathbb{R}}^n\).
MSC:
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 58A10 | Differential forms in global analysis |
| 35F05 | Linear first-order PDEs |
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
References:
| [2] | Loredana Lanzani and Elias M. Stein, A note on div curl inequalities, Math. Res. Lett. 12 (2005), no. 1, 57 – 61. · Zbl 1113.26015 · doi:10.4310/MRL.2005.v12.n1.a6 |
| [3] | Jean Van Schaftingen, Estimates for \?\textonesuperior -vector fields, C. R. Math. Acad. Sci. Paris 339 (2004), no. 3, 181 – 186 (English, with English and French summaries). · Zbl 1049.35069 · doi:10.1016/j.crma.2004.05.013 |
| [4] | H. Triebel, Interpolation theory, function spaces, differential operators, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978. Hans Triebel, Interpolation theory, function spaces, differential operators, North-Holland Mathematical Library, vol. 18, North-Holland Publishing Co., Amsterdam-New York, 1978. |
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