Two limits on Hardy and Sobolev inequalities

Abstract

It is known that classical Hardy and Sobolev inequalities hold when the exponent $p$ and the dimension $N$ satisfy $p<N<\infty$. In this note, we consider two limits of Hardy and Sobolev inequalities as $p\nearrow N$ and $N\nearrow \infty$ in some sense.

This note is submitted to RIMS Kokyuroku

Cited by in corpus (1)

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