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Symmetry results for the solutions of a partial differential equation arising in water waves

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2018 MATRIX Annals

Part of the book series: MATRIX Book Series ((MXBS,volume 3))

Abstract

This paper recalls some classical motivations in fluid dynamics leading to a partial differential equation which is prescribed on a domain whose boundary possesses two connected components, one endowed with a Dirichlet datum, and the other endowed with a Neumann datum. The problem can also be reformulated as a nonlocal problem on the component endowed with the Dirichlet datum. A series of recent symmetry results are presented and compared with the existing literature.

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Acknowledgement

The first author has been supported by the DECRA Project DE180100957 “PDEs, free boundaries and applications”. The first and third authors have been supported by the Australian Research Council Discovery Project DP170104880 “N.E.W. Nonlocal Equations atWork”. The second author has been supported by MINECO grant 18 Serena Dipierro, Pietro Miraglio and Enrico Valdinoci MTM2017-84214-C2-1-P and is part of the Catalan research group 2017 SGR 1392. Part of this work was carried out on the occasion of a very pleasant visit of the second author to the University of Western Australia, which we thank for the warm hospitality.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia

    Serena Dipierro & Enrico Valdinoci

  2. Dipartimento di Matematica, Università degli studi di Milano, Via Saldini 50, 20133, Milan, Italy

    Pietro Miraglio

  3. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Avinguda Diagonal 647, 08028, Barcelona, Spain

    Pietro Miraglio

Authors
  1. Serena Dipierro
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  2. Pietro Miraglio
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  3. Enrico Valdinoci
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Corresponding author

Correspondence to Serena Dipierro .

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Editors and Affiliations

  1. School of Mathematics and Statistics, University of Melbourne, Parkville, VIC, Australia

    Jan de Gier

  2. Department of Mathematics and Statistics, The University of Western Australia, Perth, WA, Australia

    Cheryl E. Praeger

  3. Department of Mathematics, University of California Los Angeles, Los Angeles, CA, USA

    Terence Tao

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Dipierro, S., Miraglio, P., Valdinoci, E. (2020). Symmetry results for the solutions of a partial differential equation arising in water waves. In: de Gier, J., Praeger, C., Tao, T. (eds) 2018 MATRIX Annals. MATRIX Book Series, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-030-38230-8_15

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