Symmetrization with respect to a measure
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- by Friedmar Schulz and Virginia Vera de Serio PDF
- Trans. Amer. Math. Soc. 337 (1993), 195-210 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 337 (1993), 195-210
- MSC: Primary 49Q15; Secondary 26B99, 28A20, 30C20
- DOI: https://doi.org/10.1090/S0002-9947-1993-1088477-3
- MathSciNet review: 1088477