B. Helffer, T. Hoffmann-Ostenhof
Remarks on Two Notions of Spectral Minimal Partitions
Preprint series: ESI preprints

MSC:

35B05 General behavior of solutions of PDE (comparison theorems; oscillation, zeros and growth of solutions; mean value theorems)

35J05 Laplace equation, reduced wave equation (Helmholtz), Poisson equation, See also {31Axx, 31Bxx}

35P15 Estimation of eigenvalues, upper and lower bounds

Abstract: In continuation of previous work, we analyze the properties of spectral
minimal partitions. We focus on the comparison between two
definitions of minimal partitions and give some simple rather generic
criterion implying that they cannot coincide. We illustrate this criterion
in the case of simple convex examples like the rectangle and
the equilateral triangle. This partially answers a question posed by
Bucur-Buttazzo-Henrot in 1998.


Keywords: spectral theory, minimal partitions, nodal domains