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.
|Number of pages||9|
|Journal||Journal of Mathematical Analysis and Applications|
|Publication status||Published - 2018|
All Science Journal Classification (ASJC) codes
- Applied Mathematics