Unique continuation on the boundary for Dini domains
HTML articles powered by AMS MathViewer
- by Igor Kukavica and Kaj Nyström
- Proc. Amer. Math. Soc. 126 (1998), 441-446
- DOI: https://doi.org/10.1090/S0002-9939-98-04065-9
- PDF | Request permission
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
- Frederick J. Almgren Jr., Dirichlet’s problem for multiple valued functions and the regularity of mass minimizing integral currents, Minimal submanifolds and geodesics (Proc. Japan-United States Sem., Tokyo, 1977) North-Holland, Amsterdam-New York, 1979, pp. 1–6. MR 574247
- V. Adolfsson and L. Escauriaza, $C^{1,\alpha }$ domains and unique continuation at the boundary, 1996.
- Vilhelm Adolfsson, Luis Escauriaza, and Carlos Kenig, Convex domains and unique continuation at the boundary, Rev. Mat. Iberoamericana 11 (1995), no. 3, 513–525. MR 1363203, DOI 10.4171/RMI/182
- I. Kukavica, Level sets for the stationary Ginzburg-Landau equation, 1996, to appear in Calc. Var. PDE.
- Fang-Hua Lin, Nodal sets of solutions of elliptic and parabolic equations, Comm. Pure Appl. Math. 44 (1991), no. 3, 287–308. MR 1090434, DOI 10.1002/cpa.3160440303
Bibliographic Information
- Igor Kukavica
- Affiliation: Department of Mathematics, The University of Chicago, Chicago, Illinois 60637
- Address at time of publication: Department of Mathematics, University of Southern California, Los Angeles, California 90089
- MR Author ID: 314775
- Email: kukavica@cs.uchicago.edu
- Kaj Nyström
- Affiliation: Department of Mathematics, The University of Chicago, Chicago, Illinois 60637
- Email: kaj@math.uchicago.edu
- Received by editor(s): May 13, 1996
- Received by editor(s) in revised form: July 30, 1996
- Communicated by: Christopher D. Sogge
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 441-446
- MSC (1991): Primary 31B05
- DOI: https://doi.org/10.1090/S0002-9939-98-04065-9
- MathSciNet review: 1415331