The regularity for nonlinear parabolic systems of p-Laplacian type with critical growth
The regularity for nonlinear parabolic systems of p-Laplacian type with critical growth
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DOI：
10.1016/j.jde.2014.01.018
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发表时间：
2014-04
影响因子：
2.4
通讯作者：
C. Leone;M. Misawa;A. Verde
中科院分区：
文献类型：
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作者：
C. Leone;M. Misawa;A. Verde
研究了梯度上具有临界增长的进化p-拉普拉斯系统弱解的Hölder正则性。我们建立了一个证明小解及其梯度几乎处处是局部Hölder连续的自然准则。实际上，我们的正则性结果恢复了p= 2[16]情况下的经典结果，可用于研究m维h系热流的正则性以及m-谐波流。
We study the Hölder regularity of weak solutions to the evolutionary p-Laplacian system with critical growth on the gradient. We establish a natural criterion for proving that a small solution and its gradient are locally Hölder continuous almost everywhere. Actually our regularity result recovers the classical result in the case p= 2 [16] and can be applied to study the regularity of the heat flow for m-dimensional H-systems as well as the m-harmonic flow.