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

  • Lucian Beznea
  • Mihai N. Pascu
  • Nicolae R. Pascu
Conference paper
Part of the Progress in Probability book series (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.

Keywords

Dirichlet problem Dirichlet-to-Neumann operator Infinite-dimensional Laplace operator Laplace operator Neumann problem 

1991 Mathematics Subject Classification

31B05 31B10 42B37 35J05 35J25 

Notes

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.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Lucian Beznea
    • 1
    • 2
    • 3
  • Mihai N. Pascu
    • 4
  • Nicolae R. Pascu
    • 5
  1. 1.Simion Stoilow Institute of Mathematics of the Romanian AcademyRO-014700 BucharestRomania
  2. 2.Faculty of Mathematics and Computer ScienceUniversity of BucharestBucharestRomania
  3. 3.Centre Francophone en Mathématique de BucarestBucarestRomania
  4. 4.Department of Mathematics and Computer ScienceTransilvania University of BraşovBraşovRomania
  5. 5.Department of MathematicsKennesaw State UniversityMariettaUSA

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