An Lp theory for stationary radiative transfer

Herbert Egger, Matthias Schlottbom*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

20 Citations (Scopus)

Abstract

We present a self-contained analysis of the stationary radiative transfer equation in weighted Lp spaces. The use of weighted spaces allows us to derive uniform a-priori estimates for 1 ≤ p ≤ ∞ under minimal assumptions on the parameters. By constructing an explicit example, we show that our estimates are sharp and cannot be improved in general. Better estimates are, however, derived under additional assumptions on the parameters. We also present estimates for derivatives and traces of the solution and formulate a natural energy space, for which the data-to-solution map becomes an isomorphism. As a side result, we are able to prove uniform convergence of the source iteration for all 1 ≤ p ≤ ∞ without the assumption of positive absorption that is frequently used in the literature.

Original languageEnglish
Pages (from-to)1283-1296
Number of pages14
JournalApplicable Analysis
Volume93
Issue number6
DOIs
Publication statusPublished - Jun 2014
Externally publishedYes

Keywords

  • Stationary radiative transfer
  • Vanishing absorption
  • Vanishing velocity

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