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Connections Between the Dirichlet and the Neumann Problem for Continuous and Integrable Boundary Data

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Stochastic Analysis and Related Topics

Part of the book series: Progress in Probability ((PRPR,volume 72))

Abstract

We present results concerning the representation of the solution of the Neumann problem for the Laplace operator on the n-dimensional unit ball in terms of the solution of an associated Dirichlet problem. We show that the representation holds in the case of integrable boundary data, thus providing an explicit solution of the generalized solution of the Neumann problem.

Dedicated to Rodrigo Banuelos on the occasion of his sixtieth birthday

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Acknowledgements

The first author acknowledges support from the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-III-P4-ID-PCE-2016-0372. The second author kindly acknowledges the support by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PNII-ID-PCCE-2011-2-0015.

Author information

Authors and Affiliations

  1. Simion Stoilow Institute of Mathematics of the Romanian Academy, Research Unit No. 2, P.O. Box 1-764, RO-014700 Bucharest, Romania

    Lucian Beznea

  2. Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania

    Lucian Beznea

  3. Centre Francophone en Mathématique de Bucarest, Bucarest, Romania

    Lucian Beznea

  4. Department of Mathematics and Computer Science, Transilvania University of Braşov, Str. Iuliu Maniu Nr. 50, 500091, Braşov, Romania

    Mihai N. Pascu

  5. Department of Mathematics, Kennesaw State University, 1100 S. Marietta Parkway, Marietta, GA 30060-2896, USA

    Nicolae R. Pascu

Authors
  1. Lucian Beznea
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  2. Mihai N. Pascu
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  3. Nicolae R. Pascu
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Corresponding author

Correspondence to Lucian Beznea .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Connecticut, Storrs, Connecticut, USA

    Fabrice Baudoin

  2. Department of Mathematics, Purdue University, West Lafayette, Indiana, USA

    Jonathon Peterson

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Beznea, L., Pascu, M.N., Pascu, N.R. (2017). Connections Between the Dirichlet and the Neumann Problem for Continuous and Integrable Boundary Data. In: Baudoin, F., Peterson, J. (eds) Stochastic Analysis and Related Topics. Progress in Probability, vol 72. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59671-6_4

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