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| BOUNDARY REGULARITY FOR WEAK HEAT FLOWS |
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Citation： |
LIU XIANGAO.BOUNDARY REGULARITY FOR WEAK HEAT FLOWS[J].Chinese Annals of Mathematics B,2002,23(1):119~136 |
| Page view： 1273
Net amount： 973 |
Authors： |
LIU XIANGAO; |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10071013). |
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| Abstract： |
The partial regularity of the weak heat flow of harmonic maps from a Riemannian manifold $M$ with boundary into general compact Riemannian manifold $N$ without boundary is considered. It is shown that the singular set Sing(u) of the weak heat flow satisfies $H^n_{\rho}(\Sing(u))=0$, with $n=\text{dimension} M$. Here $H^n_{\rho}$ is Hausdorff measure with respect to parabolic metric $\rho ((x,t),(y,s))=\max \{|x-y|,\sqrt{|t-s|}\}$. |
Keywords： |
weak heat flow of harmonic maps, Hardy-BMO duality, partial regularity |
Classification： |
58E20, 58J35 |
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