On smooth solutions to one phase free boundary problem in R
نویسندگان
چکیده
We construct a smooth axially symmetric solution to the classical one phase free boundary problem in R, n ≥ 3. Its free boundary is of “catenoid” type. This is a higher dimensional analogy of the HauswirthHelein-Pacard solution [18] in R. The existence of such solution is conjectured in [18, Remark 2.4]. This is the first nontrivial smooth solution to the one phase free boundary problem in higher dimensions.
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