A symmetry problem with applications to finance
2014 (English)In: Monatshefte für Mathematik (Print), ISSN 0026-9255, E-ISSN 1436-5081, Vol. 174, no 4, 617-626 p.Article in journal (Refereed) Published
In this paper we will consider an overdetermined problem in an unknown ring-shaped domain, and we prove that the domain has to be spherical ring. We will apply this problem to an n-dimensional toy model in the mean field game theory introduced by Lasry-Lions too. We show that if in Lasry-Lions model, the additional extra data ”the boundary is a level set” is assumed, then the region, where the solution is harmonic, has to have spherical symmetry.
Place, publisher, year, edition, pages
2014. Vol. 174, no 4, 617-626 p.
Mean field game, Symmetry
IdentifiersURN: urn:nbn:se:kth:diva-134810DOI: 10.1007/s00605-013-0544-8ISI: 000339875900007ScopusID: 2-s2.0-84905013340OAI: oai:DiVA.org:kth-134810DiVA: diva2:668167
QC 201409012013-11-292013-11-292014-09-01Bibliographically approved