February 8, 2024Open Access

Zero volume boundary for extension domains from Sobolev to BV

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Resumen

Abstract In this note, we prove that the boundary of a (W^1, p, BV) (W 1, p, B V) -extension domain is of volume zero under the assumption that the domain Ω is 1-fat at almost every x x ∈ ∂ Ω. Especially, the boundary of any planar (W^1, p, BV) (W 1, p, B V) -extension domain is of volume zero.

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Cite This Study

Rajala et al. (Thu,) studied this question.

synapsesocial.com/papers/68e7b92eb6db64358770f220 https://doi.org/https://doi.org/10.1007/s13163-024-00485-6

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5Lebesgue spaces of differentiable functions and distributions1961 · 314 citations

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