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Apr 10, 2019 at 0:29 vote accept Marcos
Apr 10, 2019 at 0:24 comment added Marcos That's right! Thank you for your clear explanation. In fact I did know that this function is continuous in the intermediate topology, since $\|h(t)\|_{BV} = t^{N-1}\int_{\mathbb{R}^N}|Du| + t^N \|u\|_{L^1}$. However, I'm not sure if this "weak" continuity would be enough for my purposes. Thank you anyway.
Apr 9, 2019 at 20:59 history answered Mizar CC BY-SA 4.0