For proper minimizers of parabolic variational integrals with linear growthwith respect to $|Du|$, we establish a necessary and sufficient condition for$u$ to be continuous at a point $(x_o,t_o)$, in terms of a sufficient fastdecay of the total variation of $u$ about $(x_o,t_o)$ (see (1.4) below). Theseminimizers arise also as {proper} solutions to the parabolic $1$-laplacianequation. Hence, the continuity condition continues to hold for such solutions(\S\ 3).
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机译：对于具有相对于$ | Du | $线性增长的抛物线变分积分的适当极小值，我们建立了一个必要的充分条件，使得$ u $在点（（x_o，t_o））$处连续，这取决于$ u $的总变化量约为$（x_o，t_o）$（请参阅下面的（1.4））。这些最小化器也作为抛物线$ 1-laplacian方程的{适当}解出现。因此，连续性条件对于这样的解继续成立（\ S \ 3）。
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