Geodesic
A computational approach to an optimal partition problem on surfaces
Charles M. Elliott1 orcid ; Thomas Ranner2
1University of Warwick, Coventry, UK
2University of Leeds, UK
Interfaces and free boundaries, Tome 17 (2015) no. 3, pp. 353-379

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DOI

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.
DOI : 10.4171/ifb/346
Classification : 49-XX, 35-XX, 65-XX
Mots-clés : Schrödinger equation, infinite well potential, Hardy potentials, sublinear eigenvalue type problem, flat solution, solution with compact support

Charles M. Elliott  1   ; Thomas Ranner  2

1 University of Warwick, Coventry, UK
2 University of Leeds, UK 
Charles M. Elliott; Thomas Ranner. A computational approach to an optimal partition problem on surfaces. Interfaces and free boundaries, Tome 17 (2015) no. 3, pp. 353-379. doi: 10.4171/ifb/346
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     doi = {10.4171/ifb/346},
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