LIMITS OF SOLUTIONS TO THE GENERALIZED GINZBURG-LANDAU FUNCTIONAL

ABSTRACT

We discuss the convergence issue for the generalized Ginzburg-Landau functional which penalizes the L^p -energy. We prove the strong convergence for non-integer p and obtain the obstruction for strong convergence for integer p. In the presence of obstruction, we show the limiting couple varifold is a (generalized) stationary (n ? p)-varifold.