Uniform Sobolev, interpolation and geometric Calderòn–Zygmund inequalities for graph hypersurfaces

Journal article (2024)

Authors

S. Della Corte Applied Probability - EEMCS
Antonia Diana Scuola Superiore Meridionale
Carlo Mantegazza Università degli Studi di Napoli Federico II
Research Group
Applied Probability (EEMCS) (TU Delft)
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Published Date

2024

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

Abstract

In this note, our aim is to show that families of smooth hypersurfaces of Rn+1 which are all “C1 –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” Calderòn–Zygmund inequalities.