On parabolic measures and subparabolic functions

Jang Mei G. Wu

Research output: Contribution to journalArticlepeer-review

Abstract

Let D be a domain in R n´ Rt1and ¶pD be the parabolic boundary of D. Suppose ¶pD 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 Rn+1and σ' be the (n — 1)- dimensional Hausdorff measure in Rn. and let dm(E) * dσ(E Ç B) + dσ' X dt(E Ç S) for E ⊆ ¶pD. We study (i) the relation between the parabolic measure on ¶pD and the measure dm on ¶pD and (ii) the boundary behavior of subparabolic functions on D.

Original languageEnglish (US)
Pages (from-to)171-185
Number of pages15
JournalTransactions of the American Mathematical Society
Volume251
DOIs
StatePublished - Jul 1979

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

  • Mathematics(all)
  • Applied Mathematics

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