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On “balayage inwards” of charges in $$\mathbb{R}^ n$$. (English. Russian original) Zbl 0836.31005
Math. Notes 54, No. 6, 1246-1260 (1993); translation from Mat. Zametki 54, No. 6, 90-112 (1993).
Let $$U^f$$ stand for the potential of a given density $$f$$ in a domain $$\Omega \subset \mathbb{R}^n$$. The problem is to find a distribution $$w$$ with compact support in $$\Omega$$ such that $$U^f= U^w$$ outside $$\Omega$$ and such that the support of $$w$$ is minimal in some sense. The problem is reduced to the complex analytic Cauchy problem, which is the central problem of the article. It is supposed that the boundary of $$\Omega$$ is an algebraic hypersurface in $$\mathbb{R}^n$$ and that $$f$$ has an analytic continuation to the compactification $$\mathbb{C} P^n$$ of $$\mathbb{C}^n$$.
Reviewer: M.Dont (Praha)
##### MSC:
 31B15 Potentials and capacities, extremal length and related notions in higher dimensions 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
##### Keywords:
balayage of charges; complex analytic Cauchy problem
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##### References:
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