The Stefan problem and concavity

Albert Chau, Ben Weinkove*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We construct examples for the one-phase Stefan problem which show that α-concavity of the solution is in general not preserved in time, for 0 ≤ α< 1 / 2. In particular, this shows that, in contrast to the case of the heat equation for a fixed convex domain, log concavity is not preserved for solutions of the Stefan problem.

Original languageEnglish (US)
Article number176
JournalCalculus of Variations and Partial Differential Equations
Issue number5
StatePublished - Oct 2021

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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