Uniform Sobolev, interpolation and geometric Calderón-Zygmund inequalities for graph hypersurfaces

Authors

  • Serena Della Corte
  • Antonia Diana
  • Carlo Mantegazza

DOI:

https://doi.org/10.1285/i15900932v44n1p53

Keywords:

Embedded hypersurface, Sobolev inequalities, interpolation inequalities, Calderón-Zygmund inequalities

Abstract

In this note, our aim is to show that families of smooth hypersurfaces of $\R^{n+1}$ 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" Calderón-Zygmund inequalities.

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Published

22-07-2024

Issue

Volume 44, issue 1 (2024)

Section

Articoli

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