Uniform Sobolev, interpolation and geometric Calderòn–Zygmund inequalities for graph hypersurfaces
S. Della Corte (TU Delft - Applied Probability)
Antonia Diana (Scuola Superiore Meridionale)
Carlo Mantegazza (Università degli Studi di Napoli Federico II)
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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.
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