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 Omega subset of R-N, with 1 < p < N. In particular we show that if the Finsler p-capacitary potential u associated to 0 has two homothetic level sets then 0 is Wulff shape. Moreover, we show that the concavity exponent of u is q = -(p - 1)/(N - p) if and only if Omega is Wulff shape.
Some overdetermined problems related to the anisotropic capacity / C. Bianchini, G. Ciraolo, P. Salani. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 465:1(2018), pp. 211-219. [10.1016/j.jmaa.2018.04.075]
Some overdetermined problems related to the anisotropic capacity
G. Ciraolo;
2018
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 Omega subset of R-N, with 1 < p < N. In particular we show that if the Finsler p-capacitary potential u associated to 0 has two homothetic level sets then 0 is Wulff shape. Moreover, we show that the concavity exponent of u is q = -(p - 1)/(N - p) if and only if Omega is Wulff shape.
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