Hi everyone,
I am using Mathematica v14.2 and seeking to generate solutions to simple time-independent pdes in two space dimensions, using DSolve. All the examples in the help section look fabulous but when I try to put in my own trivial equations DSolve flatly refuses to cooperate. It must be something to do with the way I am specifying my boundary conditions.

Here is a simple example:

lapeqn = Laplacian[u[x, y],{x, y}] == 0;
dcond = DirichletCondition[u[x, y] == 1, x == 0 ];
omega = Rectangle[{0, 0}, {1, 1}];
sol = FullSimplify[
  DSolve[{lapeqn, dcond}, u[x, y], {x, y} \[Element] omega]]

The result is the DSolve[] command printed out again. If I fiddle around with the Dirchlet condition, e.g.

dcond = DirichletCondition[u[x, y] == Which[x == 0, 1], True]

then Mathematica will return an analytical result (containing a Null term) but which looks like the correct answer if I set Null->0. Not satisfactory, I am missing a crucial point here. So my question is why is it so difficult to specify a Dirichlet condition on part of a 2D boundary when using DSolve? Any advice?

Cheers,
Mike