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arXiv · 1503.07928

A Necessary and Sufficient Condition for the Continuity of Local Minima of Parabolic Variational Integrals with Linear Growth

Emmanuele DiBenedetto·Ugo Gianazza·Colin Klaus
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Abstract

For proper minimizers of parabolic variational integrals with linear growth with 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 fast decay of the total variation of $u$ about $(x_o,t_o)$ (see (1.4) below). These minimizers arise also as {proper} solutions to the parabolic $1$-laplacian equation. Hence, the continuity condition continues to hold for such solutions (§ 3).

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Emmanuele DiBenedetto, Ugo Gianazza, Colin Klaus. 2015-12-01. A Necessary and Sufficient Condition for the Continuity of Local Minima of Parabolic Variational Integrals with Linear Growth. https://doi.org/10.1515/acv-2015-0014

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