The Problem of Minimal Resistance for Functions and Domains
نویسنده
چکیده
Abstract. Here we solve the problem posed by Comte and Lachand-Robert in [8] (2001). Take a bounded domain Ω ⊂ R and a piecewise smooth non-positive function u : Ω̄ → R vanishing on ∂Ω. Consider a flow of point particles falling vertically down and reflected elastically from the graph of u. It is assumed that each particle is reflected no more than once (no multiple reflections are allowed); then the resistance of the graph to the flow is expressed as R(u; Ω) = 1 |Ω| ∫
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عنوان ژورنال:
- SIAM J. Math. Analysis
دوره 46 شماره
صفحات -
تاریخ انتشار 2014