University of Oulu

Sari Lasanen, Lassi Roininen, Janne M.J. Huttunen, Elliptic boundary value problems with Gaussian white noise loads, Stochastic Processes and their Applications, Volume 128, Issue 11, 2018, Pages 3607-3627, ISSN 0304-4149,

Elliptic boundary value problems with Gaussian white noise loads

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Author: Lasanen, Sari1; Roininen, Lassi1,2; Huttunen, Janne M.J.3
Organizations: 1Sodankylä Geophysical Observatory, Tähteläntie 62 FI-99600, Finland
2Tallinn University of Technology, Department of Mathematics, Ehitajate tee 5, 19086 Tallinn, Estonia
3University of Eastern Finland, Department of Applied Physics, Yliopistonranta 1 F, FI-70211 Kuopio, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
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Language: English
Published: Elsevier, 2018
Publish Date: 2018-11-12


Linear second order elliptic boundary value problems (BVP) on bounded Lipschitz domains are studied in the case of Gaussian white noise loads. The challenging cases of Neumann and Robin BVPs are considered.

The main obstacle for usual variational methods is the irregularity of the load. In particular, the Neumann boundary values are not well-defined.

In this work, the BVP is formulated by replacing the continuity of boundary trace mappings with measurability. Instead of variational methods alone, the novel BVP derives also from Cameron–Martin space techniques.

The new BVP returns the study of irregular white noise to the study of L²-loads.

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Series: Stochastic processes and their applications
ISSN: 0304-4149
ISSN-E: 1879-209X
ISSN-L: 0304-4149
Volume: 128
Issue: 11
Pages: 3607 - 3627
DOI: 10.1016/
Type of Publication: A1 Journal article – refereed
Field of Science: 1171 Geosciences
Funding: This work has been funded by Academy of Finland (grant number 250215, Finnish Programme for Centre of Excellence in Research 2012–2017) and European Research Council (ERC advanced grant 267700 - Inverse problems).
Academy of Finland Grant Number: 250215
Detailed Information: 250215 (Academy of Finland Funding decision)
Copyright information: © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (