Abstract
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 language | English |
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Pages (from-to) | 277-284 |
Number of pages | 8 |
Journal | Potential Analysis |
Volume | 55 |
DOIs | |
Publication status | Published - 16 Jun 2020 |
Keywords
- torsion function
- Dirichlet boundary condition
- Neumann boundary condition