Abstract   This note studies the Monge–Ampere Keller–Segel equation in a periodic domain     T    d       (  d  ≥  2  )   , a fully nonlinear modification of the Keller–Segel equation where the Monge–Ampere equation   det   (  I  +    ∇    2    v  )   =  u  +  1   substitutes for the usual Poisson equation   Δ  v  =  u  . The existence of global weak solutions is obtained for this modified equation. Moreover, we prove the regularity in     L    ∞     (  0  ,  T  ;    L    ∞    ∩    W    1  ,  1  +  γ     (    T    d    )   )    for some   γ  >  0  .
['Hui Huang', 'Jian-Guo Liu']
A note on Monge–Ampère Keller–Segel equation