In this talk we report on a phenomenon that appears in extension theory of
symmetric partial differential operators in different situations: Although a
family of self-adjoint extensions possess some natural Sobolev regularity
for the functions in their domains this regularity property is suddenly lost
when the extension parameter takes a specific value. We discuss typical
examples for this sudden loss of regularity: The Krein-von Neumann extension
of a 2nd order elliptic differential expression, indefinite Laplacians on
rectangles, and Dirac operators with electrostatic delta-shell interactions.