Carleman Estimates and Unique Continuation for Second Order Parabolic Equations with Nonsmooth Coefficients
Carleman Estimates and Unique Continuation for Second Order Parabolic Equations with Nonsmooth Coefficients
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DOI：
10.1080/03605300902740395
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发表时间：
2009-01-01
影响因子：
1.9
通讯作者：
Tataru, Daniel
中科院分区：
文献类型：
--
作者：
Koch, Herbert;Tataru, Daniel
本文得到了变系数二阶抛物型方程的强唯一延拓结果。假设主部中的系数在x上满足Lipschitz条件，在时间上满足保持器条件。低阶项中的系数，即，势和梯度势，被允许是无界的，只需要满足尺度不变空间中的混合范数界。
In this work we obtain strong unique continuation results for variable coefficient second order parabolic equations. The coefficients in the principal part are assumed to satisfy a Lipschitz condition in x and a Holder [image omitted] condition in time. The coefficients in the lower order terms, i.e., the potential and the gradient potential, are allowed to be unbounded and required only to satisfy mixed norm bounds in scale invariant [image omitted] spaces.