In this thesis, an integral representation theorem is obtained for non-negative solutions of the heat equation on X = (//R)('n-1) x (0,(INFIN)) x (0,T) and their boundary behaviour is investigated by using the abstract Fatou-Naim-Doob theorem. The boundary behaviour of positive solutions of the equation Lu = 0 on Y = (//R)('n) x (0,T), where L is a uniformly parabolic second-order differential operator in divergence form is also studied. / In particular, the notion of semi-thinness is introduced for the corresponding potential theories on X and Y and relationships between fine, semi-fine and parabolic limits are obtained. / Results of Kemper specialised to X are obtained by means of fine convergence and a Carleson-type local Fatou theorem is obtained for solutions of Lu = 0 on a union of parabolic regions.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.71821 |
| Date | January 1982 |
| Creators | Mair, Bernard A. |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Mathematics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 000165637, proquestno: AAINK64491, Theses scanned by UMI/ProQuest. |
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