Ratios of harmonic functions with the same zero set
نویسندگان
چکیده
منابع مشابه
Zero Set of Sobolev Functions with Negative Power of Integrability
is of Hausdorff dimension at most n− p, by a theorem of Federer-Ziemer [3]. And for functions of bounded variation, we have Hn−1 (Σ∗) = 0, see section 5.9 of [1] for more information on fine properties of BV functions. Hence our result concerning Σ, the Lebesgue set of u of the value zero makes sense because s > n− p. In order to show Theorem 1, we will need a Poincaré type inequality which wil...
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2016
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-016-0369-4