Domain separation by means of sign changing eigenfunctions of p-Laplacians, II
- Gärtner, Klaus
- Gajewski, Herbert
2010 Mathematics Subject Classification
- 35J20 58E12
- p-Laplacian, eigenfunctions, separators
We are interested in algorithms for constructing surfaces Γ of possibly small measure that separate a given domain Ω 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 → 1, under homogeneous Neumann boundary conditions. These eigenfunctions are proven to be limits of a steepest descent methods applied to suitable norm quotients. Finally we use these ideas for the construction of separators on simplex grids.
- Nonlinear Anal., 52 (2003), no. 1, pp. 291-304