| Affiliation: | University of Minnesota, Institute for Mathematics and its Applications, Minneapolis, Minnesota 55455 Juan J. L. Velázquez ; Departamento de Matematica Aplicada, Universidad Complutense, Facultad de Matematicas 28040, Madrid, Spain |
| Abstract: | Consider an elliptic equation  in the half plane  with boundary conditions  if  and  if  where   are second and third order differential operators. It is proved that if  and, for some  ,  if  if  where  for some nonnegative integer  , then  . Results of this type are also established in case  under different conditions on  and  ; furthermore, in one case  has a lower order term which depends nonlocally on  . Such Liouville type theorems arise in the study of coating flow; in fact, they play a crucial role in the analysis of the linearized version of this problem. The methods developed in this paper are entirely different for the two cases (i)  and (ii)  ; both methods can be extended to other linear elliptic boundary value problems in a half plane. |
