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    • On Neumann eigenfunctions in lip domains 

      Burdzy, Krzysztof; Atar, Rami (American Mathematical Society, 2004)
      A "lip domain" is a planar set lying between graphs of two Lipschitz functions with constant 1. We show that the second Neumann eigenvalue is simple in every lip domain except the square. The corresponding eigenfunction ...
    • On nodal lines of Neumann eigenfunctions 

      Burdzy, Krzysztof; Atar, Rami (Institute of Mathematical Statistics, 2002-06-03)
      We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain.