We characterize the Wulff shape of an anisotropic norm in terms of solutions to overdetermined problems for the Finsler p-capacity of a convex set Ω⊂RN, with 1<p<N. In particular we show that if the Finsler p-capacitary potential u associated to Ω has two homothetic level sets then Ω is Wulff shape. Moreover, we show that the concavity exponent of u is q=−(p−1)/(N−p) if and only if Ω is Wulff shape.
Bianchini, C., Ciraolo, G., Salani, P. (2018). Some overdetermined problems related to the anisotropic capacity. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 465(1), 211-219 [10.1016/j.jmaa.2018.04.075].
Some overdetermined problems related to the anisotropic capacity
Ciraolo, Giulio
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2018-01-01
Abstract
We characterize the Wulff shape of an anisotropic norm in terms of solutions to overdetermined problems for the Finsler p-capacity of a convex set Ω⊂RN, with 1
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