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arXiv · 2304.04013

Uniform Sobolev, interpolation and geometric Calder\'on-Zygmund inequalities for graph hypersurfaces

Serena Della Corte·Antonia Diana·Carlo Mantegazza
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Abstract

In this note, our aim is to show that families of smooth hypersurfaces of $\mathbb R^{n+1}$ which are all $C^1$--close enough to a fixed compact, embedded one, have uniformly bounded constants in some relevant inequalities for mathematical analysis, like Sobolev, Gagliardo-Nirenberg and ``geometric'' Calder\'on-Zygmund inequalities. This technical result is quite useful, in particular, in the study of the geometric flows of hypersurfaces.

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Serena Della Corte, Antonia Diana, Carlo Mantegazza. 2023-04-08. Uniform Sobolev, interpolation and geometric Calder\'on-Zygmund inequalities for graph hypersurfaces. https://arxiv.org/abs/2304.04013

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