A uniqueness theorem for superharmonic functions in 𝑅ⁿ

Abstract

Abstract. Let s(x) be a nonnegative superharmonic function defined on the /i-ball B"(y; r) in R", n > 3. If s(x) tends to zero "too rapidly" as x tends to a single point £ on the boundary of B"(y; r), then we prove that s = 0. The same result can then be extended to domains D Ç R", whose boundary dD is locally C ' at £ G 3D. These results generalize some earlier work of the author and U. Kuran for n -2.