2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70417We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic term depends only on the singularities of the boundary of the domain, and give either explicit expressions or two-sided estimates for this term in a variety of situations.16 pages; no figures; replaces math.SP/0403179; completely re-writtenSpectral TheoryAnalysis of PDEs35P05; 35P15text