Gajewski, Herbert An application of eigenfunctions of \(p\)-Laplacians to domain separation. (English) Zbl 0979.35041 Math. Bohem. 126, No. 2, 395-401 (2001). Summary: We are interested in algorithms for constructing surfaces \(\Gamma \) of possibly small measure that separate a given domain \(\Omega \) into two regions of equal measure. Using the integral formula for the total gradient variation, we show that such separators can be constructed approximatively by means of sign changing eigenfunctions of the \(p\)-Laplacians, \(p \rightarrow 1\), under homogeneous Neumann boundary conditions. These eigenfunctions turn out to be limits of steepest descent methods applied to suitable norm quotients. Cited in 2 Documents MSC: 35J20 Variational methods for second-order elliptic equations 58E12 Variational problems concerning minimal surfaces (problems in two independent variables) Keywords:perimeter; relative isoperimetric inequality; \(p\)-Laplacian; eigenfunctions; steepest decent method PDF BibTeX XML Cite \textit{H. Gajewski}, Math. Bohem. 126, No. 2, 395--401 (2001; Zbl 0979.35041) Full Text: EuDML OpenURL