Critical Points and Level Sets in Exterior Boundary Problems Articles uri icon

authors

  • ENCISO, ALBERTO
  • PERALTA SALAS, DANIEL

publication date

  • June 2009

start page

  • 1947

end page

  • 1969

issue

  • 4

volume

  • 58

International Standard Serial Number (ISSN)

  • 0022-2518

Electronic International Standard Serial Number (EISSN)

  • 1943-5258

abstract

  • We study some geometrical properties of the critical set of the solutions to an exterior boundary problem in Rn/Omega, where Omega is a bounded domain with C2 connected boundary. We prove that this set can be nonempty (in fact, of codimension 3) even when Omega is contractible, thereby settling a question posed by Kawohl. We also obtain new suffcient geometric criteria for the absence of critical points in this problem and analyze the properties of the critical set for generic domains. The proofs rely on a combination of classical potential theory, transversality techniques and the geometry of real analytic sets.