Domain dependence of eigenvalues of elliptic type operators
2013 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 357, no 4, 1509-1539 p.Article in journal (Refereed) Published
The dependence on the domain for the Dirichlet eigenvalues of elliptic operators considered in bounded domains is studied. The proximity of domains is measured by a norm of the difference of two orthogonal projectors corresponding to the reference domain and the perturbed one; this allows to compare eigenvalues corresponding to domains that have non-smooth boundaries and different topology. The main result is an asymptotic formula in which the remainder is evaluated in terms of this quantity. Applications of this result are given. The results are new for the Laplace operator.
Place, publisher, year, edition, pages
Springer Verlag (Germany) , 2013. Vol. 357, no 4, 1509-1539 p.
Medical and Health Sciences
IdentifiersURN: urn:nbn:se:liu:diva-102383DOI: 10.1007/s00208-013-0947-9ISI: 000326702800011OAI: oai:DiVA.org:liu-102383DiVA: diva2:677436
Funding Agencies|Swedish Research Council (VR)||2013-12-092013-12-092013-12-09