On ``balayage inwards'' of charges in \(\mathbb{R}^ n\)
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 \(\mathbb{C}^n\).
scientific article; zbMATH DE number 795654