TY - JOUR
T1 - Renormalized Energy with Vortices Pinning Effect
AU - Shijin Ding 
JO - Journal of Partial Differential Equations
VL - 4
SP - 341
EP - 360
PY - 2000
DA - 2000/11
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5518.html
KW - Renormalized energy
KW - superconductivity
KW - vortices
KW - pinning mechanism
AB -  This paper is a continuation of the previous paper in the Journal of Partial Differential Equations [1]. We derive in this paper the renormalized energy to further determine the locations of vortices in some case for the variational problem related to the superconducting thin films having variable thickness.