Mercaldo, A.; Segura de León, S.; Trombetti, C. On the behaviour of the solutions to \(p\)-Laplacian equations as \(p\) goes to 1. (English) Zbl 1158.35024 Publ. Mat., Barc. 52, No. 2, 377-411 (2008). The authors study the behavior of the weak solutions \(u_p\) as \(p\) goes to \(1\) of the problem \[ -\text{div}(| \nabla u_p| ^{p-2}\nabla u_p) = f\;\text{ in}\;\Omega, \]\[ u_p = 0 \;\text{ on}\;\partial\Omega, \] where \(\Omega\) is an open set in \(\mathbb{R}^n\) with Lipschitz boundary and \(p>1\). The authors analyze several cases with different assumptions on \(f\); the most general assumption considered is \(f\in W^{-1,\infty}(\Omega)\). The result are illustrated by several remarks and examples. Reviewer: Marco Biroli (Milano) Cited in 28 Documents MSC: 35J20 Variational methods for second-order elliptic equations 35J70 Degenerate elliptic equations Keywords:Variational methods; Nonlinear elliptic equations; \(p\)-Laplace operator PDFBibTeX XMLCite \textit{A. Mercaldo} et al., Publ. Mat., Barc. 52, No. 2, 377--411 (2008; Zbl 1158.35024) Full Text: DOI EuDML