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.
2020
1
Agostiniani, Virginia; Mazzieri, Lorenzo
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/247224
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