On the torsion function with mixed boundary conditions

Michiel van den Berg*, Tom Carroll

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Let D be a non-empty open subset of Rm, m≥2, with boundary ∂D, with finite Lebesgue measure |D|, and which satisfies a parabolic Harnack principle. Let K be a compact, non-polar subset of D. We obtain the leading asymptotic behaviour as ε↓ 0 of the L∞ norm of the torsion function with a Neumann boundary condition on ∂D, and a Dirichlet boundary condition on ∂(εK), in terms of the first eigenvalue of the Laplacian with corresponding boundary conditions. These estimates quantify those of Burdzy, Chen and Marshall who showed that D ∖ K is a non-trap domain.
Original languageEnglish
Pages (from-to)277-284
Number of pages8
JournalPotential Analysis
Publication statusPublished - 16 Jun 2020


  • torsion function
  • Dirichlet boundary condition
  • Neumann boundary condition


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