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.
A Necessary and Sufficient Condition for the Continuity of Local Minima of Parabolic Variational Integrals with Linear Growth
GIANAZZA, UGO PIETRO
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2017-01-01
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). These minimizers arise also as proper solutions to the parabolic 1-Laplacian equation. Hence, the continuity condition continues to hold for such solutions.File in questo prodotto:
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