Heating long pipes

Dimitrios Betsakos, Alexander Yu Solynin

Research output: Contribution to journalArticlepeer-review


In this paper, we study the steady-state distribution of heat on long pipes in R3 heated along some regions of their surfaces. In particular, we prove that, if the pipe P={(x,y,z):x2+y2<1} is heated along its surface belt B(a)={(x,y,z):x2+y2=1,-a<z<a}, a> 0 , then the temperature in its cross-sections Dc={(x,y,z)∈P:z=c} is increasing in the radial direction for all c in the interval [- a, a].

Original languageEnglish
Article number40
JournalAnalysis and Mathematical Physics
Issue number1
StatePublished - Mar 2021


  • Cylindrical pipe
  • Harmonic measure
  • Heat distribution

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