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Domain Perturbation for the Solution of a Periodic Dirichlet Problem

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Current Trends in Analysis, its Applications and Computation

Part of the book series: Trends in Mathematics ((RESPERSP))

Abstract

We prove that the solution of the periodic Dirichlet problem for the Laplace equation depends real analytically on a suitable parametrization of the shape of the domain, on the periodicity parameters, and on the Dirichlet datum.

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Acknowledgements

The authors are members of the ‘Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni’ (GNAMPA) of the ‘Istituto Nazionale di Alta Matematica’ (INdAM) and acknowledge the support of the Project BIRD191739/19 ‘Sensitivity analysis of partial differential equations in the mathematical theory of electromagnetism’ of the University of Padova. P.M. also acknowledges the support of the grant ‘Challenges in Asymptotic and Shape Analysis—CASA’ of the Ca’ Foscari University of Venice.

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Authors and Affiliations

  1. Dipartimento di Matematica ‘Tullio Levi-Civita’, Università degli Studi di Padova, Padova, Italy

    Paolo Luzzini

  2. Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca’ Foscari Venezia, Venezia Mestre, Italy

    Paolo Musolino

Authors
  1. Paolo Luzzini
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  2. Paolo Musolino
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Corresponding author

Correspondence to Paolo Luzzini .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Paula Cerejeiras

  2. Institut of Applied Analysis, TU Bergakademie Freiberg, Freiberg, Germany

    Michael Reissig

  3. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Irene Sabadini

  4. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Joachim Toft

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Luzzini, P., Musolino, P. (2022). Domain Perturbation for the Solution of a Periodic Dirichlet Problem. In: Cerejeiras, P., Reissig, M., Sabadini, I., Toft, J. (eds) Current Trends in Analysis, its Applications and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-87502-2_18

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