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arXiv · 2409.01772

Smooth approximations preserving asymptotic Lipschitz bounds

Enrico Pasqualetto
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Abstract

The goal of this note is to prove that every real-valued Lipschitz function on a Banach space can be pointwise approximated on a given $\sigma$-compact set by smooth cylindrical functions whose asymptotic Lipschitz constants are controlled. This result has applications in the study of metric Sobolev and BV spaces: it implies that smooth cylindrical functions are dense in energy in these kinds of functional spaces defined over any weighted Banach space.

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Enrico Pasqualetto. 2024-09-03. Smooth approximations preserving asymptotic Lipschitz bounds. https://arxiv.org/abs/2409.01772

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