Year: 1993
Type: article
Abstract: In this paper we study the spherical symmetric rearrangement ${u^\ast }$ of a nonnegative measurable function $u$ on ${\mathbb {R}^n}$ with respect to a measure given by a nonhomogeneous density distribution $p$. Conditions on $u$ are given which guarantee that ${u^\ast }$ is continuous, of bounded variation, or absolutely continuous on lines, i.e., Sobolev regular. The energy inequality is proven in $n = 2$ dimensions by employing a Carleman type isoperimetric inequality if $\log p$ is subharmonic. The energy equality is settled via a reduction to the case of a homogeneous mass density.
Authors: Friedmar Schulz, Virginia Vera de Serio
Institution: University of Iowa
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2010354528