Abstract
In this survey, we present some recent results obtained by the authors on the asymptotic behavior of harmonic functions in a bounded domain with a small hole. Particular attention will be paid to the case of the solutions of a Dirichlet problem for the Laplace operator in a perforated domain. We fix once for all
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Acknowledgements
The research of M. Dalla Riva was supported by Portuguese funds through the CIDMA—Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT–Fundação para a Ciência e a Tecnologia”), within project UID/MAT/04106/2013. The research of M. Dalla Riva was also supported by the Portuguese Foundation for Science and Technology (“FCT–Fundação para a Ciência e a Tecnologia”) with the research grant SFRH/BPD/ 64437/2009. P. Musolino is member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The work of M. Dalla Riva and P. Musolino is also supported by “Progetto di Ateneo: Singular perturbation problems for differential operators – CPDA120171/12” of the University of Padova.
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Riva, M.D., Musolino, P. (2015). Harmonic Functions in a Domain with a Small Hole: A Functional Analytic Approach. In: Constanda, C., Kirsch, A. (eds) Integral Methods in Science and Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-16727-5_13
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DOI: https://doi.org/10.1007/978-3-319-16727-5_13
Publisher Name: Birkhäuser, Cham
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