On the rate of change of the sharp constant in the Sobolev–Poincaré inequality

Tom Carroll; Mouhamed Moustapha Fall; Jesse Ratzkin

doi:10.1002/mana.201600277

On the rate of change of the sharp constant in the Sobolev–Poincaré inequality

Tom Carroll
, Mouhamed Moustapha Fall
, Jesse Ratzkin

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

The rate of change of the sharp constant in the Sobolev–Poincaré or Friedrichs inequality is estimated for a Euclidean domain that moves outward. The key ingredients are a Hadamard variation formula and an inequality that reverses the usual Hölder inequality.

Original language	English
Pages (from-to)	2185-2197
Number of pages	13
Journal	Mathematische Nachrichten
Volume	290
Issue number	14-15
DOIs	https://doi.org/10.1002/mana.201600277
Publication status	Published - Oct 2017

Keywords

35J20
35P30
46E35
Hadamard variation
Reverse Hölder inequality
Sobolev–Poincaré inequality

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10.1002/mana.201600277

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title = "On the rate of change of the sharp constant in the Sobolev–Poincar{\'e} inequality",

abstract = "The rate of change of the sharp constant in the Sobolev–Poincar{\'e} or Friedrichs inequality is estimated for a Euclidean domain that moves outward. The key ingredients are a Hadamard variation formula and an inequality that reverses the usual H{\"o}lder inequality.",

keywords = "35J20, 35P30, 46E35, Hadamard variation, Reverse H{\"o}lder inequality, Sobolev–Poincar{\'e} inequality",

author = "Tom Carroll and Fall, \{Mouhamed Moustapha\} and Jesse Ratzkin",

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AU - Fall, Mouhamed Moustapha

AU - Ratzkin, Jesse

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AB - The rate of change of the sharp constant in the Sobolev–Poincaré or Friedrichs inequality is estimated for a Euclidean domain that moves outward. The key ingredients are a Hadamard variation formula and an inequality that reverses the usual Hölder inequality.

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KW - 35P30

KW - 46E35

KW - Hadamard variation

KW - Reverse Hölder inequality

KW - Sobolev–Poincaré inequality

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DO - 10.1002/mana.201600277

M3 - Article

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JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 14-15

ER -

On the rate of change of the sharp constant in the Sobolev–Poincaré inequality

Abstract

Keywords

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