Using the electrostatic potential u due to a uniformly charged body ⊂ Rn, n ≥ 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.
Monotonicity formulas in potential theory / Agostiniani, Virginia; Mazzieri, Lorenzo. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 2020, 59:1(2020), pp. 601-632. [10.1007/s00526-019-1665-2]
Monotonicity formulas in potential theory
Agostiniani, Virginia;Mazzieri, Lorenzo
2020-01-01
Abstract
Using the electrostatic potential u due to a uniformly charged body ⊂ Rn, n ≥ 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.File in questo prodotto:
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