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PDE Real Analysis Seminar
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
| Date, time & place | Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
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2012/05/23
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Xingfei Xiang (East China Normal University)
$L^p$ Estimates of the Vector Fields and their Applications (ENGLISH)
Xingfei Xiang (East China Normal University)
$L^p$ Estimates of the Vector Fields and their Applications (ENGLISH)
[ Abstract ]
For $1< p < \\infty$, the estimates of $W^{1,p}$ norm of the vector fields in bounded domains in $\\mathbb R^3$ in terms of their divergence and curl have been well studied. In this talk, we shall present the $L^{{3}/{2}}$ estimates of vector fields with the $L^1$ norm of the $\\curl$ in bounded domains. By a similar discussion, we establish the $L^p$ estimates of the vector fields for $1 < p < \\infty$. As an application of the $L^p$ estimates, the Global $\\dv-\\curl$ lemma in Sobolev spaces of negative indices is given.
For $1< p < \\infty$, the estimates of $W^{1,p}$ norm of the vector fields in bounded domains in $\\mathbb R^3$ in terms of their divergence and curl have been well studied. In this talk, we shall present the $L^{{3}/{2}}$ estimates of vector fields with the $L^1$ norm of the $\\curl$ in bounded domains. By a similar discussion, we establish the $L^p$ estimates of the vector fields for $1 < p < \\infty$. As an application of the $L^p$ estimates, the Global $\\dv-\\curl$ lemma in Sobolev spaces of negative indices is given.
