Exterior Dirichlet and Neumann Problems in Domains with Random Boundaries

  • Duong Thanh PhamEmail author
  • Thanh Tran
  • Dũng Dinh
  • Alexey Chernov


An approximation of statistical moments of solutions to exterior Dirichlet and Neumann problems with random boundary surfaces is investigated. A rigorous shape calculus approach has been used to approximate these statistical moments by those of the corresponding shape derivatives, which are computed by boundary integral equation methods. Examples illustrate our theoretical results.


Dirichlet and Neumann problems Random surfaces Statistical moments Shape derivative 

Mathematics Subject Classification

65N30 65N38 65N15 65N50 



Duong Thanh Pham and Dũng Dinh’s research was funded by the Department of Science and Technology–Ho Chi Minh City (HCMC-DOST), and the Institute for Computational Science and Technology (ICST) at Ho Chi Minh city, Vietnam, under Contract 21/2017/HD-KHCNTT on 21/09/2017. A part of this paper was done when Duong Pham and Dũng Dinh were working at and Thanh Tran was visiting Vietnam Institute for Advanced Study in Mathematics (VIASM). These authors thank VIASM for providing a fruitful research environment and working condition. Thanh Tran was partially supported by the Australian Research Council under the Grant DP160101755.


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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  • Duong Thanh Pham
    • 1
    • 2
    Email author
  • Thanh Tran
    • 3
  • Dũng Dinh
    • 4
  • Alexey Chernov
    • 5
  1. 1.Institute for Computational Science and TechnologyHo Chi Minh CityVietnam
  2. 2.Vietnamese German UniversityBinh Duong New CityVietnam
  3. 3.School of Mathematics and StatisticsThe University of New South WalesSydneyAustralia
  4. 4.Information Technology InstituteVietnam National University, HanoiHanoiVietnam
  5. 5.Institute for MathematicsCarl von Ossietzky UniversityOldenburgGermany

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