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Unique continuation on the boundary for Dini domains

Author(s): Igor Kukavica; Kaj Nyström
Journal: Proc. Amer. Math. Soc. 126 (1998), 441-446.
MSC (1991): Primary 31B05
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Abstract: We show that the normal derivative of a harmonic function which vanishes on an open subset of the boundary of a Dini domain cannot vanish on a subset of positive surface measure.

References:

[A]: F. J. Almgren, Jr., Dirichlet's problem for multiple valued functions and the regularity of mass minimizing integral currents, Minimal Submanifolds and Geodesics, North-Holland, Amsterdam, M. Obata, 1979, pp. 1-6. MR 82g:49038
[AE]: V. Adolfsson and L. Escauriaza, $C^{1,\alpha }$ domains and unique continuation at the boundary, 1996.
[AEK]: V. Adolfsson, L. Escauriaza, and C. Kenig, Convex domains and unique continuation at the boundary, Revista Matemática Iberoamericana 11 (1995), 513-525. MR 96j:31003
[K]: I. Kukavica, Level sets for the stationary Ginzburg-Landau equation, 1996, to appear in Calc. Var. PDE.
[L]: F.-H. Lin, Nodal sets of solutions of elliptic and parabolic equations, Comm. Pure Appl. Math. 44 (1991), 287-308. MR 92b:58224


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