Domain separation by means of sign changing eigenfunctions of p-laplacians

Abstract

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 humogeneous Neumann houndary conditions. These eigenfunctions are proven to be limtes of a steepest descent method applied to suitable norm quotients. Finally we use these ideas for the construction of separators on simplex grids.

Keywords:

• Ineqn p-Laplacian
• Eigenfunctions
• Separarors

AMS subject Classification:

• 35J20
• 58E12
• 65N99

^∗Corresponding author.

^∗Corresponding author.

Notes

^∗Corresponding author.