Global existence and uniqueness for the Lake equations with vanishing   topography : elliptic estimates for degenerate equations
  This paper deals with global existence and uniqueness for the lake equations with a bottom topography vanishing on the shore. Our result generalizes previous studies that assumed the depth to be nondegenerate. Elliptic estimates for degenerate equations has to be established studying the behavior of the associated Green function. 
Bresch Didier (LMC - IMAG), Guy Metivier (IMB)