A novel stochastic method for the solution of direct and inverse exterior elliptic problems

Charalambopoulos, Antonios; Gergidis, Leonidas

doi:10.1090/qam/1480

Authors: Antonios Charalambopoulos and Leonidas N. Gergidis
Journal: Quart. Appl. Math. 76 (2018), 65-111
MSC (2010): Primary 35J25, 60H10; Secondary 78A46
DOI: https://doi.org/10.1090/qam/1480
Published electronically: October 2, 2017
MathSciNet review: 3733095
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Abstract: A new method, in the interface of stochastic differential equations with boundary value problems, is developed in this work, aiming at representing solutions of exterior boundary value problems in terms of stochastic processes. The main effort concerns exterior harmonic problems but furthermore special attention has been paid to the investigation of time-reduced scattering processes (involving the Helmholtz operator) in the realm of low frequencies. The method, in principle, faces the construction of the solution of the direct versions of the aforementioned boundary value problems but the special features of the method assure definitely the usefulness of the approach to the solution of the corresponding inverse problems as clearly indicated herein.

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