On the Hadamard formula for nonsmooth domains
2006 (English)In: Journal of Differential Equations, ISSN 0022-0396, Vol. 230, no 2, 532-555 p.Article in journal (Refereed) Published
We consider the first eigenvalue of the Dirichlet-Laplacian in three cases: C1, 1-domains, Lipschitz domains, and bounded domains without any smoothness assumptions. Asymptotic formula for this eigenvalue is derived when domain subject arbitrary perturbations. For Lipschitz and arbitrary nonsmooth domains, the leading term in the asymptotic representation distinguishes from that in the Hardamard formula valid for smooth perturbations of smooth domains. For asymptotic analysis we propose and prove an abstract theorem demonstrating how eigenvalues vary under perturbations of both operator in Hilbert space and Hilbert space itself. This abstract theorem is of independent interest and has substantially broader field of applications. © 2006 Elsevier Inc. All rights reserved.
Place, publisher, year, edition, pages
2006. Vol. 230, no 2, 532-555 p.
IdentifiersURN: urn:nbn:se:liu:diva-37189DOI: 10.1016/j.jde.2006.08.004Local ID: 33898OAI: oai:DiVA.org:liu-37189DiVA: diva2:258038