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Two limits on Hardy and Sobolev inequalities

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arxiv 1911.04105 v1 pith:HRQCJ5OP submitted 2019-11-11 math.FA math.AP

Megumi Sano This is my paper · ORCID
classification math.FAmath.AP
keywords hardyinequalitiessobolevinftylimitsnearrowclassicalconsider
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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.

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  1. Minimization problem associated with an improved Hardy-Sobolev type inequality

    math.AP 2019-08 conditional novelty 6.0 of 10

    For an improved Hardy-Sobolev inequality on a ball, minimizers exist and are non-radial when the boundary-singular weight parameter a is close to 1, while for small a the infimum equals the classical constant and is n...

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