## Abstract

Let D be a domain in R ^{n}´ R_{t}^{1}and ¶_{p}D be the parabolic boundary of D. Suppose ¶_{p}D is composed of two parts B and S: B is given locally by t = τ and S is given locally by the graph of (formula presented here) where f is Lip 1 with respect to the local space variables and Lip 1/2 with respect to the universal time variable. Let σ be the n-dimensional Hausdorff measure in R^{n+1}and σ' be the (n — 1)- dimensional Hausdorff measure in R^{n}. and let dm(E) * dσ(E Ç B) + dσ' X dt(E Ç S) for E ⊆ ¶_{p}D. We study (i) the relation between the parabolic measure on ¶_{p}D and the measure dm on ¶_{p}D and (ii) the boundary behavior of subparabolic functions on D.

Original language | English (US) |
---|---|

Pages (from-to) | 171-185 |

Number of pages | 15 |

Journal | Transactions of the American Mathematical Society |

Volume | 251 |

DOIs | |

State | Published - Jul 1979 |

Externally published | Yes |

## Keywords

- Brownian trajectories
- Green’s function
- Hamack inequality
- Heat equation
- Lipschitz domain
- Maximum principle
- Parabolic function
- Parabolic measure
- Schauder estimates
- Subparabolic function

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics