On Inverse Problems For k-Dimensional Potentials

Siegfried Dümmel
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Siegfried Dümmel: Technische Hochschule, Sektion Mathematik

A chapter in Nonlinear Evolution Equations and Potential Theory, 1975, pp 73-88 from Springer

Abstract: Abstract Let R n(n = 3, 4, 5, …) he the n-dimensional Euclidean space, r(x, y). the distance from x∈R n to y∈R n k an integer with 1≦k≦n−1, F⊂R n a bounded k-dimensional manifold (the assumptions on F will be fixed later), ϕ a mass distribution on F, i.e., ϕ is a finite signed measure, defined, on σ-algebra of subsets of F which contains all Borel subsets of F. Then the k-dimensional potential 1.1 $${\rm u(x) = \int\limits_F {r^{2 - n} (x,y)d\varphi }} $$ is a harmonic in R n−F.

Keywords: Inverse Problem; Mass Distribution; Signed Measure; Hausdorff Measure; Borel Subset (search for similar items in EconPapers)
Date: 1975
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DOI: 10.1007/978-1-4613-4425-4_5

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