This field satisfies the Dirichlet conditions
at all four sides.
The inhomogeneous polyanalytic equation is studied by Begehr and Kumar  in D with Dirichlet conditions
and the following result is obtained.
The system (11) is accompanied with the following time-independent Dirichlet conditions
A vast literature exists on Landesman-Lazer type conditions for resonant problems in the continuous case, starting at the pioneering work  for a second order elliptic (scalar) differential equation under Dirichlet conditions
Here we have taken zero Dirichlet conditions
for illustrative purposes.
are assumed on a closed subset [[GAMMA].
1], these functional conditions include as a particular case, the Dirichlet conditions
The Robin condition is consistent with the analysis in  where it is shown that Dirichlet conditions
on inflow are preferred as v approaches 0.
Numerical comparison of strong and weak Dirichlet conditions
In this paper, we shall analyze the DGFEM applied to nonstationary convection-diffusion problems with nonlinear convection as well as diffusion and Dirichlet conditions
on non-conforming meshes.
The corresponding analysis makes use of the first Korn inequality, and hence only null Dirichlet conditions
, either on the whole boundary or on part of it, are considered.
On the physical boundaries, we impose Dirichlet conditions
according to the original equations (2.