### Abstract

Let dx denote Lebesgue measure on ℝ ^{n}. With respect to the measure C = r ^{-1} dr × dx on the collection of balls B _{r}(x) ⊂ ℝ ^{n}, the subcollection of balls B _{r}(x) ⊂ B _{1}(0) has infinite measure. Let f: B _{1}(0) → ℝ have bounded gradient, |∇f

Original language | English (US) |
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Pages (from-to) | 1641-1670 |

Number of pages | 30 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 65 |

Issue number | 12 |

DOIs | |

State | Published - Dec 1 2012 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics