1. Monotonicity formulas in potential theory
- Author
-
Virginia Agostiniani and Lorenzo Mazzieri
- Subjects
Pure mathematics ,Applied Mathematics ,35B06, 53C21, 35N25 ,010102 general mathematics ,Monotonic function ,electrostatic capacity, monotonicity formulas, quantitative Willmore inequality ,01 natural sciences ,Omega ,electrostatic capacity ,Potential theory ,010101 applied mathematics ,quantitative Willmore inequality ,Level set ,Monotone polygon ,Mathematics - Analysis of PDEs ,Flow (mathematics) ,FOS: Mathematics ,monotonicity formulas ,0101 mathematics ,Charged body ,Analysis ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
Using the electrostatic potential $u$ due to a uniformly charged body $\Omega\subset\mathbb R^n$, $n\geq 3$, we introduce a family of monotone quantities associated with the level set flow of $u$. The derived monotonicity formulas are exploited to deduce a new quantitative version of the classical Willmore inequality., Comment: This is a new version of the paper, with new proofs and enhanced results. For a detailed description of these changes we refer the reader to the Added note after the Introduction
- Published
- 2016