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ISSN 打印: 2152-5080

ISSN 在线: 2152-5099

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.7 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.9 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 0.5 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.0007 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.5 SJR: 0.584 SNIP: 0.676 CiteScore™:: 3 H-Index: 25

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ON BERNOULLI'S FREE BOUNDARY PROBLEM WITH A RANDOM BOUNDARY

卷 7, 册 4, 2017, pp. 335-353
DOI: 10.1615/Int.J.UncertaintyQuantification.2017019550
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摘要

This article is dedicated to the solution of Bernoulli's exterior free boundary problem in the situation of a random interior boundary. We provide the theoretical background that ensures the well-posedness of the problem under consideration and describe two different frameworks to define the expectation and the deviation of the resulting annular domain. The first approach is based on the Vorob'ev expectation, which can be defined for arbitrary sets. The second approach is based on the particular parametrization. In order to compare these approaches, we present analytical examples for the case of a circular interior boundary. Additionally, numerical experiments are performed for more general geometric configurations. For the numerical approximation of the expectation and the deviation, we propose a sampling method like the Monte Carlo or the quasi-Monte Carlo quadrature. Each particular realization of the free boundary is then computed by the trial method, which is a fixed-point-like iteration for the solution of Bernoulli's free boundary problem.

对本文的引用
  1. Dambrine Marc, Harbrecht Helmut, Puig Benedicte, Incorporating knowledge on the measurement noise in electrical impedance tomography, ESAIM: Control, Optimisation and Calculus of Variations, 25, 2019. Crossref

  2. Church Lewis, Djurdjevac Ana, Elliott Charles M., A domain mapping approach for elliptic equations posed on random bulk and surface domains, Numerische Mathematik, 146, 1, 2020. Crossref

  3. Dambrine M., Puig B., Oriented distance point of view on random sets, ESAIM: Control, Optimisation and Calculus of Variations, 26, 2020. Crossref

  4. Brügger Rahel, Croce Roberto, Harbrecht Helmut, Solving a Bernoulli type free boundary problem with random diffusion, ESAIM: Control, Optimisation and Calculus of Variations, 26, 2020. Crossref

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