A necessary and sufficient condition for the continuity of local minima of parabolic variational integrals with linear growth
Keyword(s):
AbstractFor 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.
1986 ◽
Vol 41
(1)
◽
pp. 115-137
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2017 ◽
Vol E100.A
(12)
◽
pp. 2764-2775
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