Gelfand problem on a large spherical cap (Q2044500)

This article discusses the behaviour of the minimal solution to the Gelfand problem on a spherical cap in \(\mathbb{R}^{N+1}\), \(N\geq 1\), under the Dirichlet boundary conditions. The asymptotic behaviour of the solution is discussed as the cap approaches the whole sphere. The approach relies on the sharp estimate of the torsion function of the spherical cap in terms of the principal eigenvalue.