Neumann Bounded Partitions of Eigenfunctions

Abstract

A new partitioning scheme, analogous to nodal domains, for the eigenfunctions of differential operators is constructed. The new scheme produces subdomains with Neumann boundaries instead of Dirichlet boundaries and will not experience an intersection avoidance phenomenon. General properties of this scheme are studied in 1 and 2 dimensions for various operators. First, a construction of the new scheme is given by providing definitions. Then numerical data is presented, and the properties of the new domains are studied. Finally, general properties are derived from the data and definitions.