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Domain dependence of eigenvalues of elliptic type operators
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2013 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 357, no 4, 1509-1539 p.Article in journal (Refereed) Published
Abstract [en]

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.
National Category
Medical and Health Sciences
URN: urn:nbn:se:liu:diva-102383DOI: 10.1007/s00208-013-0947-9ISI: 000326702800011OAI: diva2:677436

Funding Agencies|Swedish Research Council (VR)||

Available from: 2013-12-09 Created: 2013-12-09 Last updated: 2013-12-09

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Kozlov, Vladimir
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