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Stochastic Analysis and Related TopicsConnections Between the Dirichlet and the Neumann Problem for Continuous and Integrable Boundary Data

Stochastic Analysis and Related Topics: Connections Between the Dirichlet and the Neumann Problem... [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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Stochastic Analysis and Related TopicsConnections Between the Dirichlet and the Neumann Problem for Continuous and Integrable Boundary Data

Part of the Progress in Probability Book Series (volume 72)
Editors: Baudoin, Fabrice; Peterson, Jonathon
Beznea, Lucian; Pascu, Mihai N.; Pascu, Nicolae R.
Stochastic Analysis and Related Topics — Sep 27, 2017
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References (8)

Publisher
Springer International Publishing
Copyright
© Springer International Publishing AG 2017
ISBN
978-3-319-59670-9
Pages
85 –97
DOI
10.1007/978-3-319-59671-6_4
Publisher site
See Chapter on Publisher Site

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.]

Published: Sep 27, 2017

Keywords: Dirichlet problem; Dirichlet-to-Neumann operator; Infinite-dimensional Laplace operator; Laplace operator; Neumann problem; 31B05; 31B10; 42B37; 35J05; 35J25

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