A necessary and sufficient condition for the continuity of local minima of parabolic variational integrals with linear growth

作者：DiBenedetto Emmanuele; Gianazza Ugo^*; Klaus Colin

来源：Advances in Calculus of Variations, 2017, 10(3): 209-221.

DOI：10.1515/acv-2015-0014

• Continuity
• linear growth
• parabolic variational integral
• parabolic 1-Laplacian

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)). These minimizers arise also as proper solutions to the parabolic 1-Laplacian equation. Hence, the continuity condition continues to hold for such solutions.

• 出版日期2017-7-17