Greenian potentials and concavity
Let D be a bounded domain in \({\mathbb{R}}^ n\), \(v\geq 0\) be a continuous function in D and \(G_ v\) be the Green operator relative to \(- (1/2)\Delta +v\). The author proves that the corresponding Green potentials satisfy a Brunn-Minkowski type inequality and obtains the following result: If D is bounded convex and if \(f: D\to]0,\infty [\) and \(v^{-1/2}\) are concave (v\(\equiv 0\) or \(v>0)\), then \((G_ v f^ p)^{1/(2+p)}\) is concave, \(0\leq p\leq 1\).
scientific article; zbMATH DE number 3935425