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On the Hadamard Formula for Second Order Systems in Non-Smooth Domains
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
Russian Academy of Science.
2012 (English)In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 37, no 5, 901-933 p.Article in journal (Refereed) Published
Abstract [en]

Perturbations of eigenvalues of the Dirichlet problem for a second order elliptic system in a bounded domain Omega in R-n are studied under variations of the domain Omega. We investigate the case when the perturbed domain is located in a d-neighborhood of the reference Lipschitz domain. A new asymptotic formula is derived; it contains terms that are absent in the classical formula of Hadamard. The latter is valid only for smooth domains and smooth perturbations. We give conditions that guarantee the validity of the Hadamard formula. The general asymptotic formula is applied when Omega is perturbed by small curvilinear and circular cuts. Most of the results are new even for the Laplace operator.

Place, publisher, year, edition, pages
Taylor and Francis: STM, Behavioural Science and Public Health Titles / Taylor and Francis , 2012. Vol. 37, no 5, 901-933 p.
Keyword [en]
Asymptotic of eignvalues, Domain perturbations, Hadamard formula
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-77549DOI: 10.1080/03605302.2011.626100ISI: 000303236600006OAI: diva2:528344
Funding Agencies|Swedish Research Council (VR)||Linkoping University||Available from: 2012-05-25 Created: 2012-05-22 Last updated: 2012-06-07

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Kozlov, Vladimir
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