Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Unique continuation on the boundary
for Dini domains


Authors: Igor Kukavica and Kaj Nyström
Journal: Proc. Amer. Math. Soc. 126 (1998), 441-446
MSC (1991): Primary 31B05
MathSciNet review: 1415331
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [A] 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
  • [AE] V. Adolfsson and L. Escauriaza, $C^{1,\alpha }$ domains and unique continuation at the boundary, 1996.
  • [AEK] 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, 10.4171/RMI/182
  • [K] I. Kukavica, Level sets for the stationary Ginzburg-Landau equation, 1996, to appear in Calc. Var. PDE.
  • [L] Fang-Hua Lin, Nodal sets of solutions of elliptic and parabolic equations, Comm. Pure Appl. Math. 44 (1991), no. 3, 287–308. MR 1090434, 10.1002/cpa.3160440303

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 31B05

Retrieve articles in all journals with MSC (1991): 31B05


Additional 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
Email: kukavica@cs.uchicago.edu

Kaj Nyström
Affiliation: Department of Mathematics, The University of Chicago, Chicago, Illinois 60637
Email: kaj@math.uchicago.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04065-9
Received by editor(s): May 13, 1996
Received by editor(s) in revised form: July 30, 1996
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1998 American Mathematical Society