Abstract
We develop an improved version of the parabolic Lipschitz truncation, which allows qualitative control of the distributional time derivative and the preservation of zero boundary values. As a consequence, we establish a new caloric approximation lemma. We show that almost p-caloric functions are close to p-caloric functions. The distance is measured in terms of spatial gradients as well as almost uniformly in time. Both results are extended to the setting of Orlicz growth.
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Acknowledgements
These results were announced for the first time at the Mittag-Leffler Institute for the special program “Evolutionary problems”in 2013. We would like to thank the institute for the hospitality. S. Schwarzacher wishes to thank program PRVOUK P47, financed by Charles University in Prague. B. Stroffolini and A. Verde have been partially supported by the Italian M.I.U.R. Project “Calcolo delle Variazioni ” (2012).
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Communicated by J.Ball.
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Diening, L., Schwarzacher, S., Stroffolini, B. et al. Parabolic Lipschitz truncation and caloric approximation. Calc. Var. 56, 120 (2017). https://doi.org/10.1007/s00526-017-1209-6
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DOI: https://doi.org/10.1007/s00526-017-1209-6