Uniqueness set for the single-layer potential
UDC
519.63EDN
TWTYOVAbstract
The work is devoted to the question of completeness of the system of point potentials. We introduce the concept of a uniqueness set for the single-layer potential and prove that the system of point potential is complete if and only if the set of basis points (singularities) of potentials is a uniqueness set for the single-layer potential. We study properties of the introduced uniqueness sets (for the single layer potential) and give examples of sets that are uniqueness sets and those are not. We show that the new concept extends the concept of uniqueness set of harmonic functions. We give an example of a set of points, which is not a set of uniqueness of harmonic functions, however the corresponding system of point potential is complete. This set is a uniqueness set for the single-layer potential.
Keywords:
fundamental solutions method, point potentials method, basis potentials methodReferences
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Copyright (c) 2015 Свидлов А.А., Дроботенко М.И., Бирюк А.Э.
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