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Interfaces and Free Boundaries

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Volume 17, Issue 3, 2015, pp. 353–379
DOI: 10.4171/IFB/346

Published online: 2015-11-03

A computational approach to an optimal partition problem on surfaces

Charles M. Elliott[1] and Thomas Ranner[2]

(1) University of Warwick, Coventry, UK
(2) University of Leeds, UK

We explore an optimal partition problem on surfaces using a computational approach. The problem is to minimize the sum of the first Dirichlet Laplace–Beltrami operator eigenvalues over a given number of partitions of a surface. We consider a method based on eigenfunction segregation and perform calculations using modern high performance computing techniques. We first test the accuracy of the method in the case of three partitions on the sphere then explore the problem for higher numbers of partitions and on other surfaces.

Keywords: Schrödinger equation, infinite well potential, Hardy potentials, sublinear eigenvalue type problem, flat solution, solution with compact support

Elliott Charles, Ranner Thomas: A computational approach to an optimal partition problem on surfaces. Interfaces Free Bound. 17 (2015), 353-379. doi: 10.4171/IFB/346